Analog-to-Digital Converter

Description

Analog-to-digital converters (A/D converters) in automated test equipment (ATE) are required for digitizing analog signals from a device under test.

The performance of a high bandwidth analog-to-digital converter is often lim- ited by the performance of the required high frequency sampling clock. Such a high frequency sampling clock is typically generated from PLLs that suffer from jitter or phase noise impurities. The sampling clock jitter impurities may be induced into an output signal of the analog-to-digital converter and, there- fore, deteriorate the performance of high end measurement instrumentation of an automated test equipment (ATE).

It's an object of the present invention to provide an enhanced performance of a high end automated test equipment.

This object is achieved by an automated test equipment for analyzing an analog time domain output signal of an electronic device under test, wherein the automated test equipment comprises: an analog-to-digital converter configured for converting an analog time do- main signal, which is during a normal mode of operation the analog time do- main output signal of the electronic device under test, into a digital time do- main signal by obtaining a sample of the analog time domain signal at each sampling point of a plurality of sampling points; a sampling clock configured for producing a clock signal, which is fed to the analog-to-digital converter for specifying each sampling point of the plurality of sampling points over time; a time-to-frequency converter configured for converting the digital time do- main signal into a digital frequency domain signal so that the digital frequen- 5 cy domain signal is represented by frequency bins; a memory device configured for storing a set of empirically determined oper- ating parameters; and

10 a jitter components removal module for removing jitter components produced by the analog-to-digital converter in order to produce a cleaned digital fre- quency domain signal, wherein the jitter component removal module is con- figured for determining, based on the set of empirically determined operating parameters, for each frequency bin of the frequency bins an amplitude and a

15 frequency of at least one lower spur having a lower frequency than the re- spective frequency bin to which it is related to and an amplitude and a fre- quency of at least one upper spur having a higher frequency than the respec- tive frequency bin to which it is related to, wherein the jitter removal module is configured for subtracting the lower spur and the upper spur of each fre-

20 quency bin of the frequency bins from the digital frequency domain signal so that the cleaned digital frequency domain signal is produced.

When a jitter modulation of a sampling clock occurs, the sampling points dur- ing conversion get modulated in their phase with respect to the ideally regular 25 sampling grid. Thus, the analog-to-digital converter no longer samples the waveform of the analog time domain signal, which is the input signal of the analog-to-digital converter, but a different waveform that can be described mathematically by modulating the original analog time domain signal in its phase.

30

In order to simplify the description, the original and a time domain signal is assumed to be a cosine function with frequency f o = 1/To and amplitude 1 :

When samples are taken in presence of a sinusoidal jitter described with a jitter modulation function Sj(t) with a frequency of f _j and a peak-to-peak jitter 5 amplitude of T _jpp : the ideally sampled waveform, sampled across one coherency Period M*To with N samples gets disturbed according to a phase modulation:

10

with applied this yields:

15 In order to judge the impact on the spectrum of such a non-ideally sampled waveform, a trigonometric identity may be applied: with: In the given sampled signal the so called modulation index may be considered to be small i.e. , therefore the modulation is called a small band modulation and the Bessel functions of first kind and n-th order 5 J _n (r|) can be approximated:

Due to the factorial in the denominator the values of J _n decrease rapidly and therefore only the first few need to be taken into account. In most cases the io assumption: is sufficient to describe the modulation impact adequately. Therefore it is 15 possible to just look at the simple approximation of the sampled signal:

This result just means that two spurs appear in a single sided spectrum to the left and right at of the expected carrier at with a relative height to the 20 carrier of:

If s(t) is not only a simple sine wave but an arbitrary signal that gets repeated with the coherency period it is possible to express this signal in terms of its 25 Fourier series which is a linear combination of cosine terms added up to a Fourier sum:

Therefore, since s(t) is just a linear superposition of cosine functions and all jitter related relationships apply to each of the cosine terms in the Fourier 5 series, the resulting phase modulated conversion signal is therefore com- posed as follows:

In other words, the two jitter spurs are generated for each spectral compo- 10 nent of the original analog time domain signal (each cosine term) and super- impose on top of each other in a linear fashion. On the other hand, when the jitter modulation function is a generic periodic signal and is represented with more than one spectral component, another superposition occurs for all jitter modulation components in the same way. All these superpositions follow a 15 linear cumulative scheme and thus can be taken into account term by term and are finally summed up to grand total.

Whereas random jitter often is still tolerable since its disturbing energy gets spread over the whole spectral domain, the deterministic jitter is most critical 20 since all its disturbing energy gets concentrated into discrete frequency com- ponents. These discrete frequency components appear as significant spurs and may reduce the spurious free dynamic range of the conversion dramati- cally in particular for high frequency conversion signals.

25 According to the invention such deterministic jitter is removed from the output signal of the analog-to digital converter, which is the digital time domain sig- nal, by converting the digital time domain signal into a digit to frequency do- main signal so that the digital frequency domain signal is represented by fre- quency bins. As stated above it is possible in frequency domain to remove jitter components for each frequency bin independently as the jitter compo- nents of the different frequency bins are superimposed.

5

As stated above the jitter components of each frequency bin of the frequency bins may be seen as a Fourier series. However, most impact on the meas- urement have these jitter components, which are closest to the respective frequency bin. Therefore, measurements may be improved by removing of io just one lower spur and by removing of just one upper spur for each of the bins.

For that purpose the frequency and amplitude of the lower spur and the up- per spur may be calculated based on an empirically determined set of operat- 15 ing parameters, which may be stored in the memory. How such a set of op- erating parameters may be found will be discussed later in here.

The computational effort for the jitter removal is limited, since jitter cleansing procedure may be performed on the analog frequency domain signal, which

20 corresponds to the analog time domain output signal of the electronic device under test by means of a FFT which in most cases is required anyway when an analog time domain output signal analysis is requested. The effort per each analog time domain output signal processing is just the subtraction of the jitter components in each frequency bin of the digital frequency domain

25 signal. Thus, the invention provides an efficient removal of jitter components from a digital time domain signal based on an analog time domain output signal of an electronic device under test, when the automatic test equipment is in normal mode of operation.

30 According to a preferred embodiment of the invention the amplitude of the lower spur of each of the frequency bins and the amplitude of the upper spur of each of the frequency bins are calculated using a same first parameter of the set of parameters; and the frequency of the lower spur of each of the frequency bins and the fre- quency of the upper spur of each of the frequency bins are calculated using a 5 same second parameter of the set of parameters.

By these features the removal of the jitter components may be further simpli- fied.

10 According to a preferred embodiment of the invention the first parameter cor- responds to a peak-to-peak jitter amplitude of a jitter modulation function of the analog-to-digital converter and the second parameter corresponds to a jitter frequency of the jitter modulation function of the analog-to-digital con- verter.

15

With the knowledge of the peak-to-peak jitter amplitude of the jitter modula- tion function of the analog-to-digital converter and of the jitter frequency of the jitter modulation function of the analog-to-digital converter, the impact on each frequency bin, in case the respective frequency bin is filled with a spec- 20 tral component of the analog time domain output signal, may be predicted.

According to a preferred embodiment of the invention for each frequency bin the amplitude of the lower spur and the amplitude of the upper spur is calcu- lated based on the formula

25 wherein I is a number of the frequency bins, f, is the frequency of the i-th fre- quency bin, Tjpp is the peak-to-peak jitter amplitude and s _{spur i} is the amplitude of the lower spur and the amplitude of the upper spur of the i-th frequency bin relative to an amplitude of the i-th frequency bin;

30 wherein for each frequency bin the frequency of the lower spur is calculated based on the the formula is the frequency of the lower spur of the i-th frequency bin and f _j is the jitter frequency of the jitter modulation function; and wherein for each frequency bin the frequency of the upper spur is calculated 5 based on the formula is the frequency of the

upper spur of the i-th frequency bin.

Assumed an analog time domain output signal that also consists of a simple sinusoidal signal So(t) with a frequency f ₁ has to be converted with the same io sampling clock, the consequence will be that the same jitter modulation func- tion S _j (t) will now generate spurs at different frequencies and a height accord- ing to:

15 Note that the spur size changes with respect to the reference tone due to the fact that the application signal has it's spectral component at fi = 1 Ti .

Therefore, the jitter spectral components are now located at the frequencies:

20

With this result, all parameters of the spurs are determined; therefore the spurs can be removed by a simple subtraction without affecting the original application signal.

25 When the removal procedure is now performed for each frequency bin in which a signal content is detected, each frequency component of the applica- tion signal gets removed from its conversion clock jitter disturbance.

According to a preferred embodiment of the invention the automated test de- 30 vice comprises: a reference tone signal generator configured for generating a reference tone signal comprising at least one sinusoidal signal component at a given fre- quency;

5

a signal processor configured for calculating a jitter modulation function of an analog-to-digital converter of the automated test equipment by applying a Hilbert transform to a jitter modulated reference tone signal, which is the digi- tal frequency domain signal produced by the analog-to-digital converter, 10 when, during a calibration mode of operation of the automated test equip- ment, the reference tone signal is fed to the analog-to-digital converter as the analog time domain signal; and a parameter processor configured for determining the set of operating pa- is rameters based on the jitter modulation function.

Since the clock jitter disturbance is a purely additive process in which linear combinations of spectral energy are just added, the impact of clock jitter can also be removed again as long as the jitter modulation function is precisely 20 known.

Unfortunately, the jitter generation process occurs in the depth of PLLs of a clock generation integrated circuit (IC) and therefore the jitter modulation function can hardly be measured where it occurs nor it can be easily predict- 25 ed from theory. In addition the precise measurement of the disturbed high frequency conversion clock that carries the jitter is also difficult since the measurement would generate parasitic effects in the clock signal and would affect the regular performance in a negative way.

30 However, for the frequently occurring and most disturbing deterministic jitter components a measurement of a jitter modulated reference tone signal is possible in the digital time signal by means of converting a reference tone signal and performing a demodulation of the jitter modulated reference tone signal as the carrier of the jitter modulation function during a calibration mode of operation.

5 As soon as the jitter modulation function is precisely known all its spectral components can be subtracted from any spectral component of an arbitrary input signal that can be represented in terms of a finite Fourier sum.

It is evident that the jitter calibration using a reference signal works best 10 when the reference tone signal is a pure sinusoidal signal with a frequency as high as possible and the jitter modulation function is a function of only a few or better just one spectral component.

The precise determination of a sinusoidal jitter modulation function from 15 measuring the conversion result of a reference tone signal implies demodula- tion of the phase.

So if a phase-modulated sinusoidal time domain signal x(t) is given in terms of:

20 it is a purely real valued function of t. When a suitably imaginary part iy(t) may be constructed that can be added to x(t) such that a transition to the po- lar form is possible. The resulting complex function z(t) is called the analytical 25 time domain signal of x(t):

When the analytical signal of the phase-modulated signal is generated, one 30 can easily do the demodulation by simply calculating the phase (p(t) from z(t). The generation of an analytical time domain signal is possible with the Hilbert transform. This means, when the Hilbert transform to x(t) is applied, y(t) is determined. For most math libraries such as Matlab z(t) is returned complete- 5 ly during the Hilbert transform step:

In other words the phase of the jitter modulated reference tone signal may be 10 obtained by calculating:

By these features the needed set of operating parameters may be deter- 15 mined without the use of external equipment.

According to preferred embodiment of the invention the automated test de- vice comprises:

20 a connecting device connectable to a calibration device, wherein the con- necting device is configured, when being connected to the calibration device during a calibration mode of operation, for receiving a reference tone signal comprising at least one sinusoidal signal component at a given frequency from the calibration device and providing the reference tone signal to the

25 analog-to-digital converter as the analog time domain signal; a signal processor configured for calculating a jitter modulation function of an analog-to-digital converter of the automated test equipment by applying a Hilbert transform to a jitter modulated reference tone signal, which is the digi- 30 tal frequency domain signal produced by the analog-to-digital converter, when, during a calibration mode of operation of the automated test equip- ment, the reference tone signal is fed to the analog-to-digital converter as the analog time domain signal; and a parameter processor configured for determining the set of operating pa- 5 rameters based on the jitter modulation function.

In this embodiment the automatic test equipment may determine the set of operating parameter with internal means. However, the reference tone signal needs to be provided by external equipment.

10

According to preferred embodiment of the invention the signal processor is configured for calculating the jitter modulation function by using the formula wherein sj(t) represents the jitter modulation function, x(t) represents the jitter modulated reference tone sig- 15 nal, fo represents the frequency of the reference tone signal and f _j represents the jitter frequency of the jitter modulation function.

Since:

20

the obtained phase still contains the linear phase of the carrier signal. There- fore the jitter modulation function Sj(t) may finally be obtained by additionally subtracting the linear reference tone phase:

25

where x(t) is the representation of the jitter modulated reference tone signal.

30 According to a preferred embodiment of the invention the parameter proces- sor is configured for determining the first parameter and the second parame- ter of the set of parameters, wherein the first parameter corresponds to a peak-to-peak jitter amplitude of the jitter modulation function of the analog-to- digital converter and wherein the second parameter corresponds to a jitter frequency of the jitter modulation function of the analog-to-digital converter.

5

According to preferred embodiment of the invention the parameter processor is configured for determining the first parameter using the formula Tj _PP = η/(π fo), wherein T _jpp represents the peak-to-peak jitter amplitude of the jitter mod- ulation function, f ₀ represents the frequency of the reference tone signal and 10 η represents a jitter modulation index.

The jitter modulation index η actually is a well-known function of fo :

15

This means, T _jPP can be precisely determined from the frequency of the ref- erence tone signal:

20

According to a preferred embodiment of the invention the parameter proces- sor is configured for determining the second parameter by a spectral decom- position of the jitter modulation function.

25 This means one is able to extract all parameters that determine the sinusoi- dal clock jitter component.

When the jitter modulation function is perceived as a Fourier series too, where the deterministic sinusoidal jitter components are a linear sum of co- 30 sine terms, one is even able to apply the extraction procedure to all its com- ponents individually. The computational effort for the jitter removal is limited, since the jitter pa- rameter determination requiring the Hilbert transform needs to be executed only once during a calibration mode of operation of the automated test

5 equipment with a reference tone signal for the desired sampling rate. The jitter cleansing procedure may be performed on the analog time domain out- put signal's spectrum of the electronic device under test generated by means of a FFT which in most cases is required anyway when an application signal analysis is requested. The effort per each application signal processing is just

10 the subtraction of the jitter components in each frequency bin of the analog time domain output signal's spectrum of the electronic device under test.

According to a preferred embodiment of the invention the parameter proces- sor is configured for storing the set of operating parameters into a memory of 15 the automated test equipment.

By this features the calibration may be fully automated.

According to a preferred embodiment of the invention the automated test de- 20 vice comprises: a reference tone signal generator configured for generating a reference tone signal comprising at least one sinusoidal signal component at a given fre- quency; and

25

a connecting device connectable to a calibration device, wherein the con- necting device is configured, when being connected to the calibration device during a calibration mode of operation, for transmitting the digital frequency domain signal as a jitter modulated reference tone signal to the calibration 30 device. In this embodiment the automated test equipment may produce a reference tone signal by internal means. However, the calculation of the set of parame- ters needs to be done by external means.

5 According to a preferred embodiment of the invention the connecting device is configured, when being connected to the calibration device during the cali- bration mode of operation, for receiving the set of parameters from the cali- bration device and for storing the set of parameters into the memory.

10 By this features the calibration may be fully automated.

According to a preferred embodiment of the invention the automated test de- vice comprises a connecting device connectable to a calibration device ac- cording to, wherein the connecting device is configured, when being con- 15 nected to the calibration device during a calibration mode of operation, for receiving a reference tone signal from the calibration device and providing the reference tone signal to the analog-to-digital converter as the analog time domain signal; and

20

transmitting the digital frequency domain signal as a jitter modulated refer- ence tone signal to the calibration device.

According to a preferred embodiment of the invention the connecting device 25 is configured, when being connected to the calibration device during a cali- bration mode of operation, for receiving the set of parameters from the cali- bration device and for storing the set of parameters into the memory.

These features allow storing the set of operating parameters determined by 30 the external calibration device automatically into the memory of the automatic test equipment The object of the invention is achieved in a further aspect by an calibration device for empirically determining a set of operating parameters for an auto- mated test equipment, wherein the calibration device comprises:

5 a signal processor configured for calculating a jitter modulation function of an analog-to-digital converter of the automated test equipment by applying a Hilbert transform to a jitter modulated reference tone signal, which is a digital frequency domain signal produced by the analog-to-digital converter, when, during a calibration mode of operation of the automated test equipment, the

10 reference tone signal is fed to the analog-to-digital converter as an analog time domain signal; and a parameter processor configured for determining the set of operating pa- rameters based on the jitter modulation function.

15

According to preferred embodiment of the invention the calibration device comprises a reference tone signal generator configured for generating a ref- erence tone signal comprising at least one sinusoidal signal component at a given frequency.

20

Since the clock jitter disturbance is a purely additive process in which linear combinations of spectral energy are just added, the impact of clock jitter can also be removed again as long as the jitter modulation function is precisely known.

25

Unfortunately, the jitter generation process occurs in the depth of PLLs of a clock generation integrated circuit (IC) and therefore the jitter modulation function can hardly be measured where it occurs nor it can be easily predict- ed from theory. In addition the precise measurement of the disturbed high 30 frequency conversion clock that carries the jitter is also difficult since the measurement would generate parasitic effects in the clock signal and would affect the regular performance in a negative way. However, for the frequently occurring and most disturbing deterministic jitter components a measurement of a jitter modulated reference tone signal is possible in the digital time signal by means of converting a reference tone 5 signal and performing a demodulation of the jitter modulated reference tone signal as the carrier of the jitter modulation function during a calibration mode of operation.

As soon as the jitter modulation function is precisely known all its spectral io components can be subtracted from any spectral component of an arbitrary input signal that can be represented in terms of a finite Fourier sum.

It is evident that the jitter calibration using a reference signal works best when the reference tone signal is a pure sinusoidal signal with a frequency 15 as high as possible and the jitter modulation function is a function of only a few or better just one spectral component.

The precise determination of a sinusoidal jitter modulation function from measuring the conversion result of a reference tone signal implies demodula- 20 tion of the phase.

So if a phase-modulated sinusoidal time domain signal x(t) is given in terms of:

25

it is a purely real valued function of t. When a suitably imaginary part iy(t) may be constructed that can be added to x(t) such that a transition to the po- lar form is possible. The resulting complex function z(t) is called the analytical time domain signal of x(t):

30

When the analytical signal of the phase-modulated signal is generated, one can easily do the demodulation by simply calculating the phase q>(t) from z(t).

The generation of an analytical time domain signal is possible with the Hilbert transform. This means, when the Hilbert transform to x(t) is applied, y(t) is determined. For most math libraries such as Matlab z(t) is returned complete- ly during the Hilbert transform step:

In other words the phase of the jitter modulated reference tone signal may be obtained by calculating:

According to a preferred embodiment of the invention the signal processor is configured for calculating the jitter modulation function by using the formula wherein Sj(t) represents the jitter

modulation function, x(t) represents the jitter modulated reference tone sig- nal, f ₀ represents a frequency of the reference tone signal and fj represents the jitter frequency of the jitter modulation function.

Since: the obtained phase still contains the linear phase of the carrier signal. There- fore the jitter modulation function Sj(t) may finally be obtained by additionally subtracting the linear reference tone phase: where x(t) is the representation of the jitter modulated reference tone signal.

According to a preferred embodiment of the invention the calibration device is configured for determining a first parameter and a second parameter of the set of parameters, wherein the first parameter corresponds to a peak-to-peak jitter amplitude of the jitter modulation function of the analog-to-digital con- verter and wherein the second parameter corresponds to a jitter frequency of the jitter modulation function of the analog-to-digital converter.

According to a preferred embodiment of the invention the parameter proces- sor is configured for determining the first parameter using the formula T _jPP = 15 η/(π f ₀ ), wherein T _jpp represents the peak-to-peak jitter amplitude of the jitter modulation function, f ₀ represents a frequency of the reference tone signal and η represents a jitter modulation index.

The jitter modulation index η actually is a well-known function of f ₀

20

This means, T _jpp can be precisely determined from the frequency of the ref- erence tone signal:

25

According to a preferred embodiment of the invention the parameter proces- sor is configured for determining the second parameter by a spectral decom-

30 position of the jitter modulation function. This means one is able to extract all parameters that determine the sinusoi- dal clock jitter component.

When the jitter modulation function is perceived as a Fourier series too, 5 where the deterministic sinusoidal jitter components are a linear sum of co- sine terms, one is even able to apply the extraction procedure to all its com- ponents individually.

The computational effort for the jitter removal is limited, since the jitter pa- io rameter determination requiring the Hilbert transform need to be executed only once during a calibration mode of operation of the automated test equipment with a reference tone signal for the desired sampling rate. The jitter cleansing procedure may be performed on the analog time domain out- put signal's spectrum of the electronic device under test generated by means 15 of a FFT which in most cases is required anyway when an application signal analysis is requested. The effort per each application signal processing is just the subtraction of the jitter components in each frequency bin of the analog time domain output signal's spectrum of the electronic device under test.

20 According to preferred embodiment of the invention the calibration device is configured for storing the set of operating parameters into a memory of the automated test equipment.

By this features the use of the calibration device may be simplified.

25

According to a preferred embodiment of the invention the calibration device comprises a connecting device connectable to an automated test equipment in particular to an automated test equipment according to the invention, wherein the connecting device is configured, when being connected to the 30 automated test equipment during a calibration mode of operation of the au- tomated test equipment, for transmitting the reference tone signal to the automated test equipment; and receiving the jitter modulated reference tone signal from the automated test equipment.

By these features the use of the calibration device may be further simplified in case it is not an integral part of the automatic test equipment.

According to a preferred embodiment of the invention the connecting device is configured, when being connected to the automated test equipment during a calibration mode of operation of the automated test equipment, for transmit- ting the reference tone signal to the automated test equipment.

According to a preferred embodiment of the invention the connecting device is configured, when being connected to the automated test equipment during a calibration mode of operation of the automated test equipment, for transmit- ting the set of parameters to the automated test equipment.

By these features the use of the calibration device may be further simplified in case it is not an integral part of the automatic test equipment.

The object of the invention is further achieved by a system comprising an automated test equipment having a connecting device as outlined above and a calibration device having a connecting device as described above.

The object of the invention is further achieved by a method for operating an automated test equipment for analyzing an analog time domain output signal of an electronic device under test, the method comprising the steps of: converting an analog time domain signal, which is during a normal mode of operation the analog time domain output signal of the electronic device under test, into a digital time domain signal using an analog-to-digital converter ob- taining a sample of the analog time domain signal at each sampling point of a plurality of sampling points; producing a clock signal using a sampling clock, which is fed to the analog- to-digital converter for specifying each sampling point of the plurality of sam- pling points over time; converting the digital time domain signal into a digital frequency domain sig- nal using a time-to-frequency converter so that the digital frequency domain signal is represented by frequency bins; storing a set of empirically determined operating parameters a memory de- vice; and removing jitter components produced by the analog-to-digital converter in order to produce a cleaned digital frequency domain signal using a jitter components removal module, wherein, based on the set of empirically de- termined operating parameters, for each frequency bin of the frequency bins an amplitude and a frequency of at least one lower spur having a lower fre- quency than the respective frequency bin to which it is related to and an am- plitude and a frequency of at least one upper spur having a higher frequency than the respective frequency bin to which it is related to are determined, and wherein the lower spur and the upper spur of each frequency bin of the fre- quency bins are subtracted from the digital frequency domain signal so that the cleaned digital frequency domain signal is produced.

The object of the invention is further achieved by a method for empirically determining a set of operating parameters for an automated test equipment, wherein the method comprises the steps of: generating a reference tone signal comprising at least one sinusoidal signal component using a reference tone signal generator at a given frequency; establishing a jitter modulation function of an analog-to-digital converter of the automated test equipment by applying a Hilbert transform to a jitter modulated reference tone signal, which is a digital frequency domain signal produced by the analog-to-digital converter, when, during a calibration mode of operation of the automated test equipment, the reference tone signal is fed to the analog-to-digital converter as an analog time domain signal, using a signal processor; and determining the set of operating parameters based on the jitter modulation function using a parameter processor.

Moreover, the object of the invention is achieved by a computer program for performing, when running on a computer or a processor, one of the inventive methods.

Preferred embodiments of the invention are subsequently discussed with re- spect to the accompanying drawings, in which:

Fig. 1 illustrates a first embodiment of an automated test equipment according to the invention in a schematic view;

Fig. 2 shows an example of an digital frequency domain signal, which is based on digital time domain signal of an analog-to-digital

25 converter of an automated test equipment according to the in- vention, and an example of a cleaned digital frequency domain signal, which is an output signal of a jitter components removal module of an automated test equipment according to the inven- tion;

30

Fig. 3 illustrates a second embodiment of an automated test equip- ment according to the invention in a schematic view; illustrates a fourth embodiment of an automated test equipment according to the invention in a schematic view; illustrates a fifth embodiment of an automated test equipment according to the invention in a schematic view; illustrates an embodiment of a calibration device according to the invention in a schematic view; illustrates an embodiment of a method, according to the inven- tion, for operating an automated test equipment in a schematic view and an embodiment of a method, according to the inven- tion, for empirically determining a set of operating parameters for an automatic test equipment; illustrates a setup for validation of the jitter calibration concept according to the invention in a schematic view; shows a digital frequency signal based on the simulated analog time domain output signal having a frequency of 57 MHz with- out jitter injected; shows a digital frequency signal based on the simulated analog time domain output signal having a first frequency of 57 MHz and a second frequency of 63 MHz without jitter injected; shows a digital frequency signal based on the simulated analog time domain output signal having a frequency of 57 MHz with jitter having a frequency of 1 MHz injected, which was used as a reference measurement during jitter calibration; Fig. 12 shows a zoom in of the digital frequency signal shown in

Fig. 11 ;

Fig. 13 shows a jitter modulation function based on a demodulation of 5 the digital frequency signal shown in Figs. 11 and 12, wherein the jitter has an amplitude of 3.7 ps peak-to-peak;

Fig. 14 shows a digital frequency signal based on the simulated analog time domain output signal having a first frequency of 57 MHz 10 and a second frequency of 63 MHz with jitter having a frequen- cy of 1 MHz injected;

Fig. 15 shows a zoom in of the digital frequency signal shown in

Fig. 14;

15

Fig. 16 shows a cleaned digital frequency signal derived from the simu- lated analog time domain output signal having a first frequency of 57 MHz and a second frequency of 63 MHz with jitter having a frequency of 1 MHz and a 3.7 ps peak-to-peak amplitude in- 20 jected shown in Figs. 14 and 15 using a set of operating pa- rameters derived from the jitter modulation function of Fig. 13;

Fig. 17 shows a zoom in of the cleaned digital frequency signal shown in Fig. 16;

25

Fig. 18 shows a digital frequency signal with coherent jitter injected;

Fig. 19 shows a jitter modulation function based on a demodulation of the digital frequency signal shown in Fig. 18;

30

Fig. 20 shows a cleaned digital frequency signal derived from the digital frequency signal with coherent jitter injected shown in Fig. 18 using a set of operating parameters derived from the jitter mod- ulation function of Fig. 19;

Fig. 21 shows a digital frequency signal with non-coherent jitter injected having a frequency f _j of 1 MHz;

Fig. 22 shows a zoom in of the digital frequency signal shown in

Fig. 21 ;

Fig. 23 shows a jitter modulation function for the case of none-coherent jitter based on a demodulation of the digital frequency signal shown in Figs. 21 and 22;

Fig. 24 shows a zoom in of the jitter modulation function shown in

Fig. 23 wherein the zooming in shows the bin values as dots;

Fig. 25 shows a cleaned digital frequency signal derived from the digital frequency signal with non-coherent jitter injected shown in Figs. 21 and 22 using a set of operating parameters derived from the jitter modulation function of Fig. 23 an 24; and

Fig. 26 shows a zoom in of the cleaned digital frequency signal shown in Fig. 25.

Fig. 1 illustrates a first embodiment of an automated test equipment accord- ing to the invention in a schematic view.

Automated test equipment for analyzing an analog time domain output signal AOS of an electronic device under test DUT, the automated test equipment 1 comprises: an analog-to-digital converter 2 configured for converting an analog time do- main signal ATS, which is during a normal mode of operation the analog time domain output signal AOS of the electronic device under test DUT, into a dig- ital time domain signal DTS by obtaining a sample of the analog time domain signal ATS at each sampling point of a plurality of sampling points; a sampling clock 3 configured for producing a clock signal CS, which is fed to the analog-to-digital converter 2 for specifying each sampling point of the plu- rality of sampling points over time; a time-to-frequency converter 4 configured for converting the digital time do- main signal DTS into a digital frequency domain signal DFS so that the digital frequency domain signal DTS is represented by frequency bins FB1 , FB2 (see Fig.2); a memory device 5 configured for storing a set SPA of empirically determined operating parameters; and a jitter components removal module 6 for removing jitter components LS1 , LS2, US1 , US2 (see Fig.2) produced by the analog-to-digital converter 2 in order to produce a cleaned digital frequency domain signal CDFS, wherein the jitter component removal module 6 is configured for determining, based on the set SPA of empirically determined operating parameters, for each fre- quency bin FB1 , FB2 of the frequency bins FB1 , FB2 an amplitude and a frequency of at least one lower spur LS1 , LS2 having a lower frequency than the respective frequency bin FB1 , FB2 to which it is related to and an ampli- tude and a frequency of at least one upper spur US1 , US2 having a higher frequency than the respective frequency bin FB1 , FB2 to which it is related to, wherein the jitter removal module 6 is configured for subtracting the lower spur LS1 , LS2 and the upper spur US1 , US2 of each frequency bin FB1 , FB2 of the frequency bins FB1 , FB2 from the digital frequency domain signal DFS so that the cleaned digital frequency domain signal CDFS is produced. When a jitter modulation of a sampling clock 3 occurs, the sampling points during conversion get modulated in their phase with respect to the ideally regular sampling grid. Thus, the analog-to-digital converter 2 no longer sam- ples the waveform of the analog time domain signal ATS, which is the input signal ATS of the analog-to-digital converter 2, but a different waveform that can be described mathematically by modulating the original analog time do- main signal ATS in its phase.

In order to simplify the description, the analog time domain signal ATS and the digital time domain signal DTS is assumed to be a cosine function with frequency fo = 1 T ₀ and amplitude 1 :

When samples are taken in presence of a sinusoidal jitter described with a 15 jitter modulation function Sj(t) with a frequency of f _j and a peak-to-peak jitter amplitude of T _jPP : the ideally sampled waveform, sampled across one coherency Period M*T ₀ 20 with N samples gets disturbed according to a phase modulation:

with T _S = M*T ₀ /N applied this yields:

In order to judge the impact on the spectrum of such a non-ideally sampled waveform, a trigonometric identity may be applied:

5 with:

In the given sampled signal the so called modulation index may be considered to be small i.e. η « 1 , therefore the modulation is called a 10 small band modulation and the Bessel functions of first kind and n-th order can be approximated:

Due to the factorial in the denominator the values of J _n decrease rapidly and 15 therefore only the first few need to be taken into account. In most cases the assumption:

20 is sufficient to describe the modulation impact adequately. Therefore it is possible to just look at the simple approximation of the sampled signal:

This result just means that two spurs appear in a single sided spectrum to the left and right at of the expected carrier at fo ±f/fo with a relative height to the carrier of:

If s(t) is not only a simple sine wave but an arbitrary signal that gets repeated with the coherency period it is possible to express this signal in terms of its Fourier series which is a linear combination of cosine terms added up to a 10 Fourier sum:

Therefore, since s(t) is just a linear superposition of cosine functions and all jitter related relationships apply to each of the cosine terms in the Fourier 15 series, the resulting phase modulated conversion signal is therefore com- posed as follows:

In other words, the two jitter spurs LS1 and US1 for FB1 (or LS2 and US2 for 20 FB2) are generated for each spectral component FB1 , FB2 of the original analog time domain signal ATS (each cosine term) and superimpose on top of each other in a linear fashion. On the other hand, when the jitter modula- tion function is a generic periodic signal and is represented with more than one spectral component, another superposition occurs for all jitter modulation 25 components LS1 , LS2, US1 , US2 in the same way. All these superpositions follow a linear cumulative scheme and thus can be taken into account term by term and are finally summed up to grand total.

Whereas random jitter often is still tolerable since its disturbing energy gets spread over the whole spectral domain, the deterministic jitter is most critical since all its disturbing energy gets concentrated into discrete frequency com- ponents LS1 , LS2, US1 , US2. These discrete frequency components LS1 , LS2, US1 , US2 appear as significant spurs LS1 , LS2, US1 , US2 and may reduce the spurious free dynamic range of the conversion dramatically in par- ticular for high frequency conversion signals DTS.

According to the invention such deterministic jitter is removed from the output signal of the analog-to analog digital converter DTS, which is the digital time domain signal DTS, by converting the digital time domain signal DTS into a digit to frequency domain signal DFS so that the digital frequency domain signal DFS is represented by frequency bins FB1 FB2. As stated above it is possible in frequency domain to remove jitter components for each frequency bin FB1 , FB2 independently as the jitter components LS1 , LS2, US1 , US2 of the different frequency bins FB1 , FB2 are superimposed.

As stated above the jitter components of each frequency bin FB1 , FB2 of the frequency bins FB1 , FB2 may be seen as a Fourier series. However, most impact on the measurement have these jitter components LS1 , LS2, US1 , US2, which are closest to the respective frequency bin FB1 , FB2. Therefore, measurements may be improved by removing of just one lower spur LS1 , LS2 and by removing of just one upper spur US1 , US2 for each of the bins FB1 , FB2.

For that purpose the frequency and amplitude of the lower spur LS1, LS2 and

30 the upper spur US1 , US2 may be calculated based on an empirically deter- mined set of operating parameters SPA, which may be stored in the memory 5. How such a set of operating parameters SPA may be found will be dis- cussed later in here.

The computational effort for the jitter removal is limited, since jitter cleansing 5 procedure may be performed on the analog frequency domain signal DFS, which corresponds to the analog time domain output signal AOS of the elec- tronic device under test DUT and can be determined by means of a FFT which in most cases is required anyway when a frequency domain analysis of the analog time domain output signal ATS is requested. The effort per 10 each analog time domain output signal processing is just the subtraction of the jitter components LS1 , LS2, US1 , US2 in each frequency bin FB1 , FB2 of the digital frequency domain signal DFS. Thus, the invention provides an effi- cient removal of jitter components LS1 , LS2, US1, US2 from a digital time domain output signal DTS based on an analog time domain output signal of 15 an electronic device under test 1 , when the automatic test equipment 1 is in normal mode of operation.

According to a preferred embodiment of the invention the amplitude of the lower spur LS1 , LS2 of each of the frequency binsFBI , FB2 and the ampli- 20 tude of the upper spur US1 , US2 of each of the frequency bins FB1 , FB2 are calculated using a same first parameter of the set SPA of parameters; and the frequency of the lower spur LS1 , LS2 of each of the frequency bins FB1 , FB2 and the frequency of the upper spur US1 , US2 of each of the frequency 25 bins FB1 , FB2 are calculated using a same second parameter of the set SPA of parameters.

By these features the removal of the jitter components LS1 , LS2, US1 , US2 may be further simplified.

30

According to a preferred embodiment of the invention the first parameter cor- responds to a peak-to-peak jitter amplitude of a jitter modulation function JMF of the analog-to-digital converter 2 and the second parameter corresponds to a jitter frequency of the jitter modulation function JMF of the analog-to-digital converter 2.

5 With the knowledge of the peak-to-peak jitter amplitude of the jitter modula- tion function JMF of the analog-to-digital converter 2 and of the jitter frequen- cy of the jitter modulation function JMF of the analog-to-digital converter 2, the impact on each frequency bin FB1 , FB2, in case the respective frequency bin FB1, FB2 is filled with a spectral component of the analog time domain io output signal AOS, may be predicted.

According to a preferred embodiment of the invention for each frequency bin FB1 , FB2 the amplitude of the lower spur LS1 , LS2 and the amplitude of the upper spur US1 , US2 is calculated based on the formula

15 wherein I is a number of the frequency bins FB1 ,

FB2, f _j is the frequency of the i-th frequency bin FB1 , FB2, T _jpp is the peak-to- peak jitter amplitude and s _spur i is the amplitude of the lower spur LS1 , LS2 and the amplitude of the upper spur US1 , US2 of the i-th frequency bin FB1 , FB2 relative to an amplitude of the i-th frequency bin FB1 , FB2;

20

wherein for each frequency bin FB1 , FB2 the frequency of the lower spur LS1 , LS2 is calculated based on the the formula

is the frequency of the lower spurLS1 , LS2 of the i-th frequency bin FB1 , FB2 and f _j is the jitter frequency of the jitter modulation function JMF; and

25

wherein for each frequency bin FB1 , FB2 the frequency of the upper spur US1 , US2 is calculated based on the formula

the frequency of the upper spur US1 , US2 of the i-th frequency bin FB1 , FB2.

30 Assumed an analog time domain output signal AOS that also consists of a simple sinusoidal signal s ₀ (t) with a frequency f _i has to be converted with the same sampling clock 3, the consequence will be that the same jitter modula- tion function Sj(t) will now generate spurs LS and US at different frequencies and a height according to:

5

Note that the spur size changes with respect to the reference tone due to the fact that the application signal has its spectral component at fi = 1/ΤΊ . There- fore, the jitter spectral components are now located at the frequencies:

10

With this result, all parameters of the spurs LS and US are determined for all frequency bins FB; therefore the spurs can be removed by a simple subtrac- tion in the frequency domain without affecting the original application signal 15 AOS.

When the removal procedure is now performed for each frequency bin FB1 , FB2 in which a signal content is detected, each frequency component of the application signal AOS gets removed from its conversion clock jitter disturb- 20 ance.

Fig. 2 shows an example of a digital frequency domain signal DFS, which is based on digital time domain signal DTS of an analog-to-digital converter 2 of an automated test equipment 1 according to the invention, and an example of 25 a cleaned digital frequency domain signal CDFS, which is an output signal of a jitter components removal module 6 of an automated test equipment ac- cording to the invention.

Fig. 3 illustrates a second embodiment of an automated test equipment 1 30 according to the invention in a schematic view. According to a preferred embodiment of the invention the automated test de- vice 1 comprises:

5 a reference tone signal generator 9 configured for generating a reference tone signal RTS comprising at least one sinusoidal signal component at a given frequency; a signal processor 11 configured for calculating a jitter modulation function 10 JMF of an analog-to-digital converter 2 of the automated test equipment 1 by applying a Hilbert transform to a jitter modulated reference tone signal JMS, which is the digital frequency domain signal DFS produced by the analog-to- digital converter 2, when, during a calibration mode of operation of the auto- mated test equipment 1 , the reference tone signal RTS is fed to the analog- 15 to-digital converter 2 as the analog time domain signal ATS; and a parameter processor 12 configured for determining the set SPA of operat- ing parameters based on the jitter modulation function JMF.

20 Since the clock jitter disturbance is a purely additive process in which linear combinations of spectral energy are just added, the impact of clock jitter can also be removed again in the frequency domain as long as the jitter modula- tion function is precisely known.

25 Unfortunately, the jitter generation process occurs in the depth of PLLs of a clock generation integrated circuit (IC) and therefore the jitter modulation function JMF can hardly be measured where it occurs nor it can be easily predicted from theory. In addition the precise measurement of the disturbed high frequency conversion clock that carries the jitter is also difficult since the

30 measurement would generate parasitic effects in the clock signal CS and would affect the regular performance in a negative way. However, for the frequently occurring and most disturbing deterministic jitter components a measurement of a jitter modulated reference tone signal JMS is possible in the digital time signal DTS by means of converting a reference tone signal RTS and performing a demodulation of the jitter modulated refer- 5 ence tone JMS signal as the carrier of the jitter modulation function JMF dur- ing a calibration mode of operation.

As soon as the jitter modulation function JMF is precisely known all its spec- tral components can be subtracted from any spectral component of an arbi- 10 trary input signal that can be represented in terms of a finite Fourier sum.

It is evident that the jitter calibration using a reference signal works best when the reference tone signal is a pure sinusoidal signal with a frequency as high as possible and the jitter modulation function is a function of only a 15 few or better just one spectral component.

The precise determination of a sinusoidal jitter modulation function JMF from measuring the conversion result of a reference tone signal RTS implies de- modulation of the phase.

20

So if a phase-modulated sinusoidal time domain signal x(t) is given in terms of:

25 it is a purely real valued function of t. When a suitably imaginary part iy(t) may be constructed that can be added to x(t) such that a transition to the po- lar form is possible. The resulting complex function z(t) is called the analytical time domain signal of x(t):

30

When the analytical signal of the phase-modulated signal is generated, one can easily do the demodulation by simply calculating the phase φ(ί) from z(t).

5 The generation of an analytical time domain signal is possible with the Hilbert transform. This means, when the Hilbert transform to x(t) is applied, y(t) is determined. For most math libraries such as Matlab z(t) is returned complete- ly during the Hilbert transform step: io

In other words the phase of the jitter modulated reference tone signal JMS may be obtained by calculating:

15

By these features the needed set SPA of operating parameters may be de- termined without the use of external equipment.

According to a preferred embodiment of the invention the signal processor 11 20 is configured for calculating the jitter modulation function JMF by using the formula wherein Sj(t) represents the jitter modulation function JMF, x(t) represents the jitter modulated refer- ence tone signal JMS, fo represents the frequency of the reference tone sig- nal RTS and f _j represents the jitter frequency of the jitter modulation function 25 JMF.

Since:

30 the obtained phase still contains the linear phase of the carrier signal. There- fore the jitter modulation function Sj(t) may finally be obtained by additionally subtracting the linear reference tone phase:

5

where x(t) is the representation of the jitter modulated reference tone signal JMS. io According to a preferred embodiment of the invention the parameter proces- sor 12 is configured for determining a first parameter and a second parame- ter of the set of parameters SPA, wherein the first parameter corresponds to a peak-to-peak jitter amplitude of the jitter modulation function JMF of the analog-to-digital converter 2 and wherein the second parameter corresponds

15 to a jitter frequency of the jitter modulation function JMF of the analog-to- digital converter 2.

According to a preferred embodiment of the invention the parameter proces- sor 12 is configured for determining the first parameter using the formula T _jpp 20 = η/π f ₀ , wherein T _jpp represents the peak-to-peak jitter amplitude of the jitter modulation function JMF, fo represents the frequency of the reference tone signal RTS and η represents a jitter modulation index.

The jitter modulation index η actually is a well-known function of fo :

25

This means, T _jPP can be precisely determined from the frequency of the ref- erence tone signal:

30 According to preferred embodiment of the invention the parameter processor 12 is configured for determining the second parameter by a spectral decom- position of the jitter modulation function JMF.

5

This means one is able to extract all parameters that determine the sinusoi- dal clock jitter component.

When the jitter modulation function is perceived as a Fourier series too, io where the deterministic sinusoidal jitter components are a linear sum of co- sine terms, one is even able to apply the extraction procedure to all its com- ponents individually.

The computational effort for the jitter removal is limited, since the jitter pa- is rameter determination requiring the Hilbert transform need to be executed only once during a calibration mode of operation of the automated test equipment 1 with a reference tone signal RTS for the desired sampling rate. The jitter cleansing procedure may be performed on the analog time domain output signal's AOS spectrum of the electronic device under test DUT gener- 20 ated by means of a FFT which in most cases is required anyway when an application signal AOS analysis is requested. The effort per each application signal AOS processing is just the subtraction of the jitter components L1 , L2, US1, US2 in each frequency bin FB1 , FB2 of the analog time domain output signal's AOS spectrum of the electronic device under test DUT.

25

According to a preferred embodiment of the invention parameter processor 12 is configured for storing the set SPA of operating parameters into a memory 5 of the automated test equipment 1.

30 By this features the use the calibration may be simplified. Fig. 4 illustrates a fifth embodiment of an automated test equipment 1 ac- cording to the invention in a schematic view.

According to a preferred embodiment of the invention the automated test de- 5 vice 1 comprises: a connecting device 8 connectable to a calibration device 7, wherein the connecting device 8 is configured, when being connected to the calibration device 7 during a calibration mode of operation, for receiving a reference 10 tone signal RTS comprising at least one sinusoidal signal component at a given frequency from the calibration device 7 and providing the reference tone signal RTS to the analog-to-digital converter 2 as the analog time do- main signal ATS;

15 a signal processor 11 configured for calculating a jitter modulation function JMF of an analog-to-digital converter 2 of the automated test equipment 1 by applying a Hilbert transform to a jitter modulated reference tone signal JMS, which is the digital frequency domain signal DFS produced by the analog-to- digital converter 2, when, during a calibration mode of operation of the auto-

20 mated test equipment 1 , the reference tone signal RTS is fed to the analog- to-digital converter 2 as the analog time domain signal ATS; and a parameter processor 12 configured for determining the set SPA of operat- ing parameters based on the jitter modulation function JMF.

25

In this embodiment the automatic test equipment 1 may determine the set SPA of operating parameter with internal means. However, the reference tone signal RTS needs to be provided by external equipment 7. The signal processor 11 and a parameter processor 12 may be configured as explained 30 with respect to Fig. 3. By the connecting device 8 the calibration device 7 may be easily connected to the automated test equipment in order to determine the needed set SPA of operating parameters.

5 According to a preferred embodiment of the invention (not shown in the fig- ures) the automated test device 1 comprises: a reference tone signal generator 9 configured for generating a reference tone signal RTS comprising at least one sinusoidal signal component at a 10 given frequency; and a connecting device 8 connectable to a calibration device 7, wherein the connecting device 8 is configured, when being connected to the calibration device 7 during a calibration mode of operation, for transmitting the digital 15 frequency domain signal DFS as a jitter modulated reference tone signal JMS to the calibration device 7.

In this embodiment the automated test equipment 1 may produce a reference tone signal CS by internal means. However, the calculation of the set of pa- 20 rameters SPA needs to be done by external means 7.

The reference tone signal generator 9 may be configured as explained with respect to Fig. 3.

25 By the connecting device 8 the calibration device 7 may be easily connected to the automated test equipment 1 in order to determine the needed set SPA of operating parameters.

Fig. 5 illustrates a fifth embodiment of an automatic test equipment 1 accord- 30 ing to the invention in a schematic view. According to a preferred embodiment of the invention the automated test de- vice 1 comprises: a connecting device 8 connectable to a calibration device 7 according to one 5 of the claims 14 or 15, wherein the connecting device 8 is configured, when being connected to the calibration device 7 during a calibration mode of op- eration, for receiving a reference tone signal RTS from the calibration device 7 and 10 providing the reference tone signal RTS to the analog-to-digital converter 2 as the analog time domain signal ATS; transmitting the digital time domain signal DTS as a jitter modulated refer- ence tone signal JMS to the calibration device 7.

15

According to a preferred embodiment of the invention the connecting device 8 is configured, when being connected to the calibration device 7 during the calibration mode of operation, for receiving the set of parameters SPA from the calibration device 7 and for storing the set of parameters SPA into the 20 memory 5.

These features allow storing the set of operating parameters determined by the external calibration device automatically into the memory of the automatic test equipment

25

Fig. 6 illustrates an embodiment of a calibration device 7 according to the invention in a schematic view.

The calibration device 7 comprises:

30

a signal processor 11 configured for calculating a jitter modulation function JMF of an analog-to-digital converter 2 of the automated test equipment 1 by applying a Hilbert transform to a jitter modulated reference tone signal JMS, which is a digital time frequency signal DFS produced by the analog-to-digital converter 2, when, during a calibration mode of operation of the automated test equipment 1 , the reference tone signal RTS is fed to the analog-to-digital converter 2 as an analog time domain signal ATS; and a parameter processor 12 configured for determining the set SPA of operat- ing parameters based on the jitter modulation function JMF.

According to preferred embodiment of the invention the concentration device comprises a reference tone signal generator 9 configured for generating a reference tone signal RTS comprising at least one sinusoidal signal compo- nent at a given frequency.

Since the clock jitter disturbance is a purely additive process in which linear combinations of spectral energy are just added, the impact of clock jitter can also be removed again in the frequency domain as long as the jitter modula- tion function is precisely known.

Unfortunately, the jitter generation process occurs in the depth of PLLs of a clock generation integrated circuit (IC) and therefore the jitter modulation function JMF can hardly be measured where it occurs nor it can be easily predicted from theory. In addition the precise measurement of the disturbed high frequency conversion clock that carries the jitter is also difficult since the measurement would generate parasitic effects in the clock signal CS and would affect the regular performance in a negative way.

However, for the frequently occurring and most disturbing deterministic jitter components a measurement of a jitter modulated reference tone signal JMS is possible in the digital time signal DTS by means of converting a reference tone signal RTS and performing a demodulation of the jitter modulated refer- ence tone JMS signal as the carrier of the jitter modulation function JMF dur- ing a calibration mode of operation.

As soon as the jitter modulation function JMF is precisely known all its spec- 5 tral components can be subtracted from any spectral component of an arbi- trary input signal that can be represented in terms of a finite Fourier sum.

It is evident that the jitter calibration using a reference signal works best when the reference tone signal is a pure sinusoidal signal with a frequency io as high as possible and the jitter modulation function is a function of only a few or better just one spectral component.

The precise determination of a sinusoidal jitter modulation function JMF from measuring the conversion result of a reference tone signal RTS implies de- 15 modulation of the phase.

So if a phase-modulated sinusoidal time domain signal x(t) is given in terms of:

20

it is a purely real valued function of t. When a suitably imaginary part iy(t) may be constructed that can be added to x(t) such that a transition to the po- lar form is possible. Phe resulting complex function z(t) is called the analytical time domain signal of x(t):

25

p )

When the analytical signal of the phase-modulated signal is generated, one can easily do the demodulation by simply calculating the phase (p(t) from z(t).

30 The generation of an analytical time domain signal is possible with the Hilbert transform. This means, when the Hilbert transform to x(t) is applied, y(t) is determined. For most math libraries such as Matlab z(t) is returned complete- ly during the Hilbert transform step:

In other words the phase of the jitter modulated reference tone signal JMS may be obtained by calculating:

According to a preferred embodiment of the invention the signal processor 11 is configured for calculating the jitter modulation function JMF by using the formula ) represents the jitter modulation function JMF, x(t) represents the jitter modulated refer- ence tone signal JMS, f ₀ represents the frequency of the reference tone sig- nal RTS and f _j represents the jitter frequency of the jitter modulation function JMF.

Since: the obtained phase still contains the linear phase of the carrier signal. There- fore the jitter modulation function Sj(t) may finally be obtained by additionally subtracting the linear reference tone phase:

30 where x(t) is the representation of the jitter modulated reference tone signal JMS.

According to a preferred embodiment of the invention the calibration device 7 is configured for determining a first parameter and a second parameter of the set of parameters SPA, wherein the first parameter corresponds to a peak-to- peak jitter amplitude of the jitter modulation function JMF of the analog-to- digital converter 2 and wherein the second parameter corresponds to a jitter frequency of the jitter modulation function JMF of the analog-to-digital con- verter 2.

According to a preferred embodiment of the invention the parameter proces- sor 12 is configured for determining the first parameter using the formula T _jpp = η/π f ₀ , wherein T _jpp represents the peak-to-peak jitter amplitude of the jitter modulation function JMF, f ₀ represents the frequency of the reference tone signal RTS and η represents a jitter modulation index.

The jitter modulation index η actually is a well-known function of fo :

This means, T _jpp can be precisely determined from the frequency of the ref- erence tone signal:

According to preferred embodiment of the invention the parameter processor 12 is configured for determining the second parameter by a spectral decom- position of the jitter modulation function JMF. This means one is able to extract all parameters that determine the sinusoi- dal clock jitter component.

When the jitter modulation function is perceived as a Fourier series too, 5 where the deterministic sinusoidal jitter components are a linear sum of co- sine terms, one is even able to apply the extraction procedure to all its com- ponents individually.

The computational effort for the jitter removal is limited, since the jitter pa- io rameter determination requiring the Hilbert transform need to be executed only once during a calibration mode of operation of the automated test equipment 1 with a reference tone signal RTS for the desired sampling rate. The jitter cleansing procedure may be performed on the analog time domain output signal's AOS spectrum of the electronic device under test DUT gener- is ated by means of a FFT which in most cases is required anyway when an application signal AOS analysis is requested. The effort per each application signal AOS processing is just the subtraction of the jitter components L1 , L2, US1, US2 in each frequency bin FB1 , FB2 of the analog time domain output signal's AOS spectrum of the electronic device under test DUT.

20

According to a preferred embodiment of the invention the calibration device 7 is configured for storing the set SPA of operating parameters into a memory 5 of the automated test equipment 1.

25 By this features the use of the calibration device 7 may be simplified.

According to a preferred embodiment of the invention the calibration device 7 comprises a connecting device 13 connectable to an automated test equip- ment 1 , in particular to an automated test equipment 1 according to the in- 30 vention, wherein the connecting device 13 is configured, when being con- nected to the automated test equipment 1 during a calibration mode of opera- tion of the automated test equipment 1 , for transmitting the reference tone signal RTS to the automated test equipment 1 ; receiving the jitter modulated reference tone signal JMS from the automated test equipment 1.

By these features the use of the calibration device 7 may be further simplified in case it is not an integral part of the automatic test equipment 1.

According to a preferred embodiment of the invention the connecting device 13 is configured, when being connected to the automated test equipment 1 during a calibration mode of operation of the automated test equipment 1 , for transmitting the reference tone signal RTS to the automated test equipment 1.

According to a preferred embodiment of the invention the connecting device 13 is configured, when being connected to the automated test equipment 1 during a calibration mode of operation of the automated test equipment 1 , for transmitting the set SPA of parameters to the automated test equipment 1.

By these features the use of the calibration device 7 may be further simplified in case it is not an integral part of the automatic test equipment.

Fig. 7 illustrates an embodiment of a method 14, according to the invention, for operating an automated test equipment 1 in a schematic view and an em- bodiment of a method 15, according to the invention, for empirically determin- ing a set of operating parameters SPA for an automatic test equipment 1.

The method 14 comprises the steps of: converting an analog time domain signal ATS, which is during a normal mode of operation the analog time domain output signal AOS of the electronic de- vice under test DUT, into a digital time domain signal DTS using an analog- to-digital converter 2 obtaining a sample of the analog time domain signal ATS at each sampling point of a plurality of sampling points; producing a clock signal CS using a sampling clock 3, which is fed to the analog-to-digital converter 2 for specifying each sampling point of the plurality of sampling points over time; converting the digital time domain signal DTS into a digital frequency domain signal DFS using a time-to-frequency converter 4 so that the digital frequency domain signal DFS is represented by frequency bins FB1 , FB2; storing a set SPA of empirically determined operating parameters a memory device 5; and removing jitter components LS1 , LS2, US1, US2 produced by the analog-to- digital converter 2 in order to produce a cleaned digital frequency domain signal CDFS using a jitter components removal module 6, wherein, based on the set SPA of empirically determined operating parameters, for each fre- quency bin FB1, FB2 of the frequency bins FB1, FB2 an amplitude and a fre- quency of at least one lower spur LS1 , LS2 having a lower frequency than the respective frequency bin FB1 , FB2 to which it is related to and an ampli- tude and a frequency of at least one upper spur US1 , US2 having a higher frequency than the respective frequency bin FB1, FB2 to which it is related to are determined, and wherein the lower spur LS1 , LS2 and the upper spur US1 , US2 of each frequency bin FB1 , FB2 of the frequency bins FB1 , FB2 are subtracted from the digital frequency domain signal DFS so that the cleaned digital frequency domain signal CDTS is produced.

The method 15 comprises the steps of: generating a reference tone signal RTS comprising at least one sinusoidal signal component at a given frequency using a reference tone signal genera- tor 9; establishing a jitter modulation function JMF of an analog-to-digital converter 2 of the automated test equipment 1 by applying a Hilbert transform to a jitter modulated reference tone signal JMS, which is a digital frequency domain signal DFS produced by the analog-to-digital converter 2, when, during a cal- ibration mode of operation of the automated test equipment 1 , the reference tone signal RTS is fed to the analog-to-digital converter 2 as an analog time domain signal ATS, using a signal processor11 ; and determining the set SPA of operating parameters based on the jitter modula- tion function JMF using a parameter processor 12.

Fig. 8 illustrates a setup for validation of the jitter calibration concept accord- ing to the invention in a schematic view.

For validation of the jitter calibration concept a dedicated setup was created using an automated test equipment high speed digitizer instrument contain- ing a 250Msps 16bit analog-to-digital converter 2. The set up comprises an analog time domain output signal simulator 16 having a first sine generator and a second sine generator The outputs of two pure sine wave generators generating a 57MHz and a 63MHz tone respectively were combined to form a simulated signal AOSs as it may occur during device test. This signal AOSs was routed to the analog input of the digitizer instrument 2 running at a data rate of 150Msps. The frequencies of the signal AOSs were chosen to be co- herent with the sample rate; this means the accurate numbers were

56.996154785MHz and 63.002014160MHz respectively. The jitter frequency however was chosen to be 1MHz exactly, resulting in a non-coherent jitter.

A branch-off cable was attached to the termination resistor at the clock input of the analog-to digital converter 2 to obtain a precisely controlled jitter injec- tion capability into the conversion clock. The branch-off cable was terminated at the other end and a jitter source 17 was attached to one leg of the differen- tial termination, injecting common mode noise which gets translated into ex- aggerated conversion clock jitter. The jitter source was programmed to inject 5 a 1 MHz sinusoidal jitter.

In a first step the reference measurement was taken with the 57MHz sine wave as a single tone signal and the 63MHz tone was turned off. The jitter frequency and the amplitude was extracted from this reference measurement io according to the jitter demodulation method deploying the Hilbert transform.

The jitter modulation function was precisely extracted with a 1MHz jitter fre- quency and a 3.7ps pk-pk amplitude.

In a next step these jitter parameters were used to calculate the jitter caused 15 for each frequency bin FB1, FB2 and the induced jitter LS1, LS2, US1, US2 for all bins FB1, FB2 in the spectrum was removed according to their per bin amplitude and frequency. After the execution of the jitter removal procedure the injected jitter LS1 , LS2, US1 , US2 was no longer visible and the dual tone signal was obtained in its original form. Only a small amount of processing 20 artefacts that are all smaller than -80dB und thus negligible were obtained. It therefore can be concluded, that the jitter calibration concept is working properly.

Fig. 9 shows the digital frequency signal DFSs based on the simulated ana- 25 log time domain output signal AOSs having a frequency of 57 MHz without jitter injected.

Fig. 10 shows the digital frequency signal DFSs based on the simulated ana- log time domain output signal AOSs having a first frequency of 57 MHz and a 30 second frequency of 63 MHz without jitter injected. Fig. 11 shows the digital frequency signal DFSs based on the simulated ana- log time domain output signal AOSs having a frequency of 57 MHz with jitter having a frequency of 1 MHz injected, which was used as a reference meas- urement during jitter calibration.

Fig. 12 shows a zoom in of the digital frequency signal DFSs shown in Fig. 11.

Fig. 13 shows the jitter modulation function JMFs based on a demodulation of the digital frequency signal DFSs shown in Figs. 11 and 12, wherein the jitter has an amplitude of 3.7 ps peak-to-peak.

Fig. 14 shows a digital frequency signal DFSs based on the simulated analog time domain output signal AOSs having a first frequency of 57 MHz and a second frequency of 63 MHz with jitter having a frequency of 1 MHz injected.

Fig. 15 shows a zoom in of the digital frequency signal DFSs shown in Fig. 14.

Fig. 16 shows a cleaned digital frequency signal CDFSs derived from the simulated analog time domain output signal AOSs having a first frequency of 57 MHz and a second frequency of 63 MHz with jitter having a frequency of 1 MHz and a 3.7 ps peak-to-peak amplitude injected shown in Figs. 14 and 15 using a set of operating parameters derived from the jitter modulation func- tion JMFs of Fig. 13.

Fig. 17 shows a zoom in of the cleaned digital frequency signal CDFs shown in Fig. 16.

30 Fig. 18 shows a digital frequency signal with coherent jitter injected. One specific aspect during the reference tone jitter calibration is the coheren- cy of the spectral components contained in the jitter modulation function JMF. In case the jitter modulation is sinusoidal and just contains one spectral com- ponent energy leakage to side bins will occur for the modulation peaks when the jitter modulation function JMF is not coherent with respect to the coher- ency period selected for the application signal AOSs. As a consequence the jitter modulation function JMF no longer contains just one spectral compo- nent but several bins will be filled with jitter components. Since the jitter mod- ulation function JMF is rarely linked in a coherent way to the sampling pro- cess it is therefore required that the jitter modulation impact is treated for each leakage bin as it is described above for the main jitter bin. This treat- ment can be perceived as if the non-coherent jitter modulation function is re- peated with the coherency period and needs therefore be represented with a Fourier series that reflects the leakage skirt rather than with just one sinusoi- dal function.

To get the full understanding of the coherency subject, the jitter calibration algorithm was executed on the above reference signal but with the signal generated mathematically. A coherent and non-coherent jitter was injected and removed respectively for comparison.

As it can be seen coherent jitter (fs=150Msps, N=32768, M=13451 , f=56.996154785MHz, Mj=223, fj=1.020812988MHz) maps into a single bin and the demodulated jitter also contains energy in just one bin at the jitter frequency. In such a theoretical case, the removal may be restricted to just one jitter bin.

The more realistic case of non-coherent jitter (fs=150Msps, N=32768, M=13451 , f=56.996154785MHz, fj=1 MHz) however shows the energy leak- age into neighboring bins. In such a case not just one jitter bin has to be tak- en into account for removal but several bins and a reasonable limit has to be established for the number of relevant bins used for jitter removal. In the demonstrated case jitter bins beyond -90dB were taken into account for re- moval. With this experiment it becomes evident, that even non-coherent jitter is efficiently removed from the converted signal using the described jitter cal- ibration method.

5

Fig. 19 shows a jitter modulation function JMFs based on a demodulation of the digital frequency signal DFSs shown in Fig. 18.

Fig. 20 shows a cleaned digital frequency signal CDFSs derived from the io digital frequency signal DFSs with coherent jitter injected shown in Fig. 18 using a set SPA of operating parameters derived from the jitter modulation function JMF of Fig. 19.

Fig. 21 shows a digital frequency signal DFSs with non-coherent jitter inject- 15 ed having a frequency f _j of 1 MHz.

Fig. 22 shows a zoom in of the digital frequency signal DFSs shown in Fig. 21.

20 Fig. 23 shows a jitter modulation function JMFs for the case of none-coherent jitter based on a demodulation of the digital frequency signal shown in Figs. 21 and 22.

Fig. 24 shows a zoom in of the jitter modulation function JMFs shown in 25 Fig. 23 wherein the zooming in shows the bin values as dots.

Fig. 25 shows a cleaned digital frequency signal CDFSs derived from the digital frequency signal DFSs with non-coherent jitter injected shown in Figs. 21 and 22 using a set SPA of operating parameters derived from the jitter 30 modulation function JMFs of Fig. 23 an 24. Fig. 26 shows a zoom in of the cleaned digital frequency signal CDFSs shown in Fig. 25.

With respect to the devices and the methods of the described embodiments the following shall be mentioned:

Although some aspects have been described in the context of an apparatus, it is clear that these aspects also represent a description of the correspond- ing method, where a block or device corresponds to a method step or a fea- ture of a method step. Analogously, aspects described in the context of a method step also represent a description of a corresponding block or item or feature of a corresponding apparatus.

Depending on certain implementation requirements, embodiments of the in- vention can be implemented in hardware or in software. The implementation can be performed using a digital storage medium, for example a floppy disk, a DVD, a CD, a ROM, a PROM, an EPROM, an EEPROM or a FLASH memory, having electronically readable control signals stored thereon, which cooperate (or are capable of cooperating) with a programmable computer system such that the respective method is performed.

Some embodiments according to the invention comprise a data carrier hav- ing electronically readable control signals, which are capable of cooperating with a programmable computer system such that one of the methods de- scribed herein is performed.

Generally, embodiments of the present invention can be implemented as a computer program product with a program code, the program code being operative for performing one of the methods when the computer program product runs on a computer. The program code may for example be stored on a machine readable carrier. Other embodiments comprise the computer program for performing one of the methods described herein, which is stored on a machine readable carrier or a non-transitory storage medium.

In other words, an embodiment of the inventive method is, therefore, a com- puter program having a program code for performing one of the methods de- scribed herein, when the computer program runs on a computer.

A further embodiment of the inventive methods is, therefore, a data carrier (or a digital storage medium, or a computer-readable medium) comprising, rec- orded thereon, the computer program for performing one of the methods de- scribed herein.

A further embodiment of the inventive method is, therefore, a data stream or a sequence of signals representing the computer program for performing one of the methods described herein. The data stream or the sequence of signals may be configured, for example, to be transferred via a data communication connection, for example via the Internet.

A further embodiment comprises a processing means, for example a com- puter, or a programmable logic device, configured or adapted to perform one of the methods described herein.

A further embodiment comprises a computer having installed thereon the computer program for performing one of the methods described herein.

In some embodiments, a programmable logic device (for example a field pro- grammable gate array) may be used to perform some or all of the functionali- ties of the methods described herein. In some embodiments, a field pro- grammable gate array may cooperate with a microprocessor in order to per- form one of the methods described herein. Generally, the methods are ad- vantageously performed by any hardware apparatus. While this invention has been described in terms of several embodiments, there are alterations, permutations, and equivalents which fall within the scope of this invention. It should also be noted that there are many alterna- 5 tive ways of implementing the methods and compositions of the present in- vention. It is therefore intended that the following appended claims be inter- preted as including all such alterations, permutations and equivalents as fall within the true spirit and scope of the present invention. io Reference signs:

1 automated test equipment

2 analog-to-digital converter

15 3 sampling clock

4 time-to-frequency converter

5 memory

6 jitter components removal module

7 calibration device

20 8 connecting device

9 reference tone signal generator

11 signal processor

12 parameter processor

13 connecting device

25 14 method for operating an automated test equipment

15 for empirically determining a set of operating parameters for an auto- matic test equipment

16 analog time domain output signal simulator

17 jitter source

30

AOS analog time domain output signal

DUT device under test ATS analog time domain signal

DTS digital time domain signal

CS clock signal

DFS digital frequency domain signal

CDFS cleaned digital frequency domain signal

SPA set of parameters

FB frequency bin

LS lower spur

US upper spur

RTS reference tone signal

JMS jitter modulated reference tone signal

JMF jitter modulation function

AOSs analog time domain output signal (simulated)

DFSs digital frequency domain signal (based on the simulated analog time domain output signal)

JMFs jitter modulation function (based on the simulated analog time domain output signal)