Field of the Invention

This invention relates generally to calculating the enthalpy of a body of gas or humid air for use in heating and air conditioning systems. In particular, this invention relates to the use of a circuit to model an equation that allows enthalpy to be calculated from sensed temperature and relative humidity.

Background of the Invention

Economizer based control schemes used in commercial air conditioning equipment take advantage of what is referred to as "free" cooling. In other words, when external air may be used for cooling, it is desirable to control a damper to adjust the amount of exterior air being utilized. Some of these economizer systems use dry bulb temperature to decide if the outdoor air is suitable for use. Other systems use enthalpy as a basis for this decision. A system using the enthalpy of the air is more efficient than one relying only on temperature, because enthalpy is a measure of the energy in the air. Accordingly, it is desirable to provide a device to calculate enthalpy from temperature and humidity.

Some prior art systems which use both temperature and relative humidity to control a damper utilize a mechanical humidity sensor. The mechanical humidity sensor is connected to a temperature sensing element and a mechanical link which actuates a mechanical switch.

Another prior art enthalpy sensor utilizes an electronic humidity sensor and an electronic temperature sensor. The output of the sensors are provided to a digital circuit and a look-up table is accessed, thereby obtaining an enthalpy value for the sensed values. However, the accuracy of a look up table is limited by its size and provides a "stepped" output rather than a

continuous output, and the cost of a look up table increases with size. Accordingly, an enthalpy calculator that has a look up table to determine enthalpy is not useful over a wide range of temperature and humidities, because either the cost of the look up table will be prohibitive or the enthalpy calculations will have a significant error.

Another prior art system described in U.S. Patent No. 4,672,560, issued June 9, 1987, to Katayama et al., discloses an enthalpy calculator which provides a circuit to model an enthalpy calculation. However, the enthalpy calculation modeled therein is a linear approximation of a more precise equation. Accordingly, the approximation and the circuit implementing the approximation are limited by their range of use and accuracy. For example, as described in U.S. Patent No. 4,672,560, the range of temperatures the equation is accurate for is from 20-30°C. Such a range is not broad enough for use in a system where the enthalpy will be used to determine whether or not to control a damper and utilize outside air.

In view of the prior art deficiencies noted above it is desirable to provide an enthalpy calculator that provides a continuous output, rather than a stepped output such as that from a look-up table. Preferably the enthalpy calculator will model an equation to provide an enthalpy value that is accurate over a wide range of temperature and humidity. Thus, the enthalpy calculator should model a substantially exact equation rather than merely a linear approximation.

SUMMARY OF THE INVENTION An enthalpy calculator according to the invention comprises a temperature sensor having an output RT indicative of temperature, a humidity sensor having an output CS indicative of humidity, and an electronic circuit having RT as a first input and the CS a second

input; wherein the circuit provides an output h of the form: h = Kl + K2*F1(RT) + K3*F2(CS) + K4*F1(RT) *F2(CS) In accordance with one embodiment of this invention, an enthalpy calculator includes a temperature sensitive resistor having a resistance RT and a relative humidity sensitive capacitor wherein the capacitance of the relative humidity sensitive capacitor is CS.

VR + — VRl + CS— (1) h = — ^{C1 C1}

₊ / CS+C2\ I FB * RO \ \ Cl j \ RO + RT j where FB, VR, C2, Cl, VRl, and RO are circuit parameters. In accordance with another embodiment of this invention an enthalpy calculator includes a temperature sensitive resistor having a resistance RT and a relative humidity sensitive capacitor wherein the capacitance of the relative humidity sensitive capacitor is CS. An electronic circuit includes RT and CS and provides an output h

(2 ) h = VR ₊ - * VRl - C2 VX*RO ₊ CS _ CS ^ VX*RO

Cl Cl RO+RT Cl Cl RO+RT

where VX, VR, C2, Cl, VRl, and RO are circuit parameters. According to a second embodiment of the present invention an enthalpy calculator also includes a temperature sensitive resistor having a resistance RT and a relative humidity sensitive capacitor having a capacitance CS. An electronic circuit includes RT and CS and models the equation:

, . , , . 6 . 2198 * RH* P _W A T) (3 ) h = 0 . 240 * t + (1061 + 0 .444 * t) * ^ws

RH* „_ ( D 14 .721 + - *-

100

According to a third embodiment of the present invention a system for controlling an environmental parameter of a room comprises a source of energy controlled air and a source of external air. A damper is connected to the source of external air and the source of

energy controlled air. The position of the damper determines the amount of external air and energy controlled air provided to the room. A control circuit controls the position of the damper and includes either of the enthalpy calculators described above to determine whether the external air is suitable to be used.

According to yet another embodiment of the present invention a method for controlling an environmental parameter of a room includes the steps of providing energy controlled air and external air. The temperature and humidity of the controlled and external air is sensed, and an electronic circuit calculates the enthalpy from the temperature and humidity using equation 3 above. The suitability of external air is determined in response to the calculated enthalpies.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a schematic diagram of an enthalpy calculator 100 constructed in accordance with one embodiment of the present invention; Figure 2 is a schematic diagram of an alternative enthalpy calculator 200;

Figure 3 is a schematic diagram of the amplifier of the enthalpy calculator of Figure 2; and Figure 4 is a schematic diagram of the preferred embodiment of the enthalpy calculator constructed in accordance with the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

As stated above, enthalpy is a measure of the energy content of the air based on both the dry bulb temperature and the moisture content of the air. This invention includes a device that measures both the dry bulb temperature and the moisture content of the surrounding air and provides a signal that represents enthalpy. The enthalpy value is obtained by calculating enthalpy from temperature and humidity using a widely

accepted equation. The calculation is performed using an analog circuit that accurately models the equation.

The following equations may be found in the ASHRAE Fundamentals Handbook and define enthalpy (h) in terms of temperature and relative humidity.

6.2198* RH* P„ _S ( T)

(4) h = 0.240 * t + (1061 + 0.444* t) *

RH* P _W A T)

14.721 +

100 where the enthalpy is measured in BTUs/lb, t is the temperature in degrees Fahrenheit, RH is the percent relative humidity, and

where P is given in inches of H ₂ 0 and T is the temperature in degrees R. The coefficients in equation (5) have the following values: al = -10440.39708 a4 = 1.289036 * 10" ⁵ a2 = -11.2946496 a5 = -2.478068 * 10" ⁹ a3 = -2.7022355 * 10 ^"2 a6 = 6.5459673 To model equation (4) the inventors have designed a circuit that has an output voltage VOUT defined as follows:

(6) VOUT = Kl + K2*Fl ( t) + K3*F2 (RH) + K4 *Fl { t) *F2 (RH)

Where Kl, K2, K3 and K4 are constants defined by circuit parameters and, Fl(t) is a function of temperature, and F2 (RH) is a function of relative humidity. A circuit having such an output voltage will accurately model the enthalpy equation where enthalpy is calculated as a function of sensed relative humidity (RH) and sensed temperature (t) . Referring now to Figure 1, a schematic diagram of an enthalpy calculator 100 constructed in accordance with the preferred embodiment of the present invention is shown. As will be described in greater detail below, the circuit configuration and component values are selected

to provide an output voltage VOUT which has a magnitude corresponding to enthalpy for the given input humidity and temperatures. In the preferred embodiment 0 to 5 volts at VOUT corresponds linearly to an enthalpy of 0 to 150 BTUs/lb.

Enthalpy calculator 100 includes a plurality of voltage sources VX, VRl and VR, a temperature dependent resistor RT, a pair of resistors RO and Rl, a plurality of switches SW1, SW2 , SW3 and SW4, a plurality of capacitors Cl, C2, C3 and CF, a humidity dependent capacitor CS, and an OP amp Al, As will be described in greater detail below, the circuit models equations (4) and (5) , thereby providing an output indicative of the enthalpy. Temperature dependent resistor RT is a thermistor in the preferred embodiment, and may be implemented using a Fenwall Unicurve temperature sensor whose resistance R(T) in ohms is a function of temperature as:

[- b * T - -T/T « -xjb ^z « ^~ ♦ i *c - i *c*T*a _. 2. c* r J

where a, b and c are constants.

Capacitor CS is a temperature dependent capacitor such as a Johnson Controls, Inc. all polymer humidity sensor having JCI Code No. HUM-1000-1, whose characteristics (capacitance as a function of humidity) may be described as a second order polynomial equation as shown below:

(8) CS = CO + cl *RH + C2*RH ² where the capacitance is given in picofarads and RH is the percent relative humidity. cO, cl and c2 are constants having the following values: CO = 204.37 X 10 ^"12 cl = .313 x 10- ¹² c2 = -.00061011 x 10 •12

Each of switches SW1-SW4 is a single pole, double throw (SPDT) switch, and they share a single controlling clock. Moreover, switches SW1-SW4 are in phase such that at any given time either all four switches connect a Z terminal to a Yl terminal (position 1) or all four switches connect the Z terminal to a YO terminal.

The clock frequency is fixed and is slow enough to ensure that all of the capacitors in the circuit can completely charge and discharge during each cycle. The inventors have determined that 8.5 KHz is appropriate for one embodiment, but one skilled in the art will readily recognize that other switching frequencies are equally acceptable. First, the description of the circuit operation will be given for the time period when the switches are in position 1. Switches SW1 and SW2 connect capacitor C2 to voltage source VRl and to voltage source VX through temperature dependent resistor RT. Voltage source VRl is a source of constant DC voltage, as is voltage source VX. The voltage at a node VT (the Yl terminal of switch SW1) is given by the voltage divider comprised of temperature dependent resistor RT and resistor RO. Thus, the steady state voltage at that node will be equal to:

(9) VT - ^VX * ^R0

RO + RT The voltage across C2 is VT - VRl. Accordingly, the charge on capacitor C2 is: C2*(VT-VR1) =

C2*(VX*R0/(RO+RT)-VRl) . Of course, as stated above, this equation assumes that the capacitors had time to completely charge and there is no leakage through them. Voltage VT is also provided through switch SW3 to capacitor C3 and humidity dependent capacitor CS. Thus, the voltage across capacitors C3 and CS will be VT- VR. Capacitor C3 is selected to have a much greater capacitance than capacitor CS and AC couples capacitor CS to the Z terminal of SW3. The voltage on capacitor C3 will reach a steady state DC value equal to (VT-VR)/2,

therefore the voltage on capacitor CS will also be equal to (VT-VR)/2. At this point the charge on CS will be equal to CS*(VT-VR)/2.

Capacitor CF is connected between the circuit output (VOUT) and the inverting input of OP amp Al. The voltage on capacitor CF will be (VR-VOUT) because voltage source VR is connected to the non-inverting input of OP amp Al. The charge on CF will be CF*(VR-VOUT) ,

Capacitor Cl is connected to output voltage VOUT through switch SW4 and is connected at its other terminal to voltage source VR. Accordingly, the voltage across capacitor Cl will be VOUT-VR, and the amount of charge on capacitor Cl is Cl*(VOUT-VR) .

When the switches SW1-SW4 change to position 2 (connecting terminals Z and YO) , capacitors Cl and C2 are connected in parallel to each other and are also connected in parallel with the series connection of C3 and CS. Since the output of Al will change such that its negative and positive inputs are equal and are at VR, the voltage across capacitors Cl, C2 and C3+CS will be forced to be zero. Since C3 is very large and its voltage does not change, the voltage on CS will change from (VT-VR)/2 to -(VT-VR)/2. Therefore, the change in voltage on CS will be (VT-VR) and the charge transfer will be CS*(VT- VR) . The total charge on C2, CS and Cl will be

(10) QT = C2* ( VT-VR1 ) + CS* ( VT-VR) + Cl * ( VOUT-VR)

and this net charge will be transferred to capacitor CF which is in the feedback loop of OP amp Al.

When charge QT is transferred to capacitor CF, the voltage across capacitor CF, V(CF) , changes. This voltage is given by V(CF) = VR - VOUT + Δ VOUT, where Δ

VOUT is the amount that the voltage across capacitor CF must change when charge QT is transferred to it. Δ VOUT

= QT/CF.

When Δ VOUT is equal to 0, then the circuit has reached a steady state condition. At such time the total charge QT must also be 0 and thus 0=Q2+QS+Q1.

Substituting for the charges, 0=C2*(VT-VR1) + CS*(VT-VR) + Cl*(VOUT-VR) .

Solving this equation for VOUT gives:

(11) VOUT ^~ VR+— *VR1 - — *VT + — *VR - — *VT

Cl Cl Cl Cl

As may be seen, the equation above for VOUT, which describes the output of the circuit of Figure 1, has the form of equation 6 above, where VR, VRl, C2 and Cl determine constants K1-K4 and VT corresponds to Fl(t) and CS corresponds to F2(RH) . Thus, the circuit of Figure 1 may be used to accurately model the enthalpy equation.

As will be described in detail later, the component values should be chosen by minimizing the error between the circuit output VOUT and a scaled value of enthalpy for the range of humidity and temperature values desired. For the circuit of Figure 1 and the following circuit parameters were selected:

VR=1.54 VT=(VX*R0)/(RO+RT)

VRl=-3.023 VX=-0.493

C2=150 PFD R0=2100 Cl=56 PFD where RT is the thermistor described above.

Referring now to Figure 2, a schematic diagram of an alternative enthalpy calculator 200 constructed in accordance with the invention is shown. Enthalpy calculator 200 includes all of the components of the embodiment of Figure 1, but further includes a feedback amplifier A2 having a gain of FB, and a summer SI.

Amplifier A2 receives as an input VOUT and multiplies that value by FB. The product is provided to summer SI, where it is summed with VX and provided to temperature dependent resistor RT.

Thus, the voltage at node VT will be equal to the sum of voltages VX+FB*V0UT divided by the voltage divider. In other words,

(12) XT - ^RO * ^{( VX + FB} * ^V0UT )

RO + RT

The remaining portions of the circuit operate identically as in Figure 1. Therefore, the output equation will be the same, except that VX in the definition of VT above is replaced by (VX+FB*V0UT) . Making this substitution and solving for VOUT results in:

VR+ - VRl + CS ™ - ^CS+C2 * ^VX * ^R0 (13) VOUT = ∞- ^{C1 C1 RO+RT}

C CSS++CC22\\ I I FB * RO Cl j \ RO + RT

Equation 13 may be re-written in a more general form as:

(14) VOUT = ^{K1 + K2} * ^F1 - t) ⁺ K3 *F2 (RH) + K4 *Fl ( t) *F2 (RH)

1 + K5*Fl ( t) + K6*Fl ( t) *F2 (RH)

Referring now to Figure 3 the circuit used to implement A2 of Figure 3 is shown. Letting VX equal 0 results in the circuit of Figure 3 where A2 is comprised of an operational amplifier A3 and input resistor RI and a feedback resistor RF. The input resistor is connected to the voltage divider formed by resistors RT and RO, which are connected between VOUT and ground. Analysis of this circuit yields the gain FB of amplifier A2 as negative RF/RI.

As shown in Figure 4, the circuit of Figure 3 has been combined with the circuit of 2 and 1 to produce an enthalpy calculator including an amplifier A3. Figure 4 differs from Figure 2 in that voltage source VX has been eliminated and resistor RT is connected to output VOUT through amplifier A3. Input resistor RI is connected between node VT and the inverting input of OP amp A3. Feedback resistor RF is connected across the output and inverting input of OP amp A3, and the non- inverting input of OP amp A3 is connected to ground.

Accordingly, OP amp A3 provides a gain of, and multiplies VT by, -RF/RI. The output of OP amp A3, -(VT*RF/RI) is provided to the Yl terminals of switches SW1 and SW3. With VX = 0, equation 13 above becomes:

VR + m^m VRl + CS— ( 15 ) VOUT = ^{C1 C1}

I CS+C2 \ I FB * RO \ Cl I \ RO + RT }

To determine circuit components that result in accurate enthalpy calculations, known values of enthalpy for a range of temperatures and humidities were used to produce a matrix from which the variables (circuit component values) may be calculated. This was done as will be described below.

First, the range of temperatures of interest was selected to be 55°F to 105°F, and the range of relative humidities of interest was selected to be from 0 to 100%. The step in temperature was chosen to be 15° and the step in relative humidity was chosen to be 10%.

Given equation 8 above for the capacitance as a function of relative humidity for the humidity sensor CS, and equation 7 for the resistance as a function of temperature for temperature sensor RT, the circuit values that minimize the error for an enthalpy output may be calculated.

However, equation 7 above, which gives the resistance of the thermistor RT as a function of temperature, was based on a temperature T in degrees Kelvin. The following equation 16 is analogous to equation 8, but is based on a temperature t in degrees F

Where a = .0015168834 b = 2.1955575994 X 10" ⁴

C = 2.4154651819 X 10" ⁶

To solve the variables an input matrix B is used where bO = VRl, bl = VR and b2 = VX. The circuit unknowns and the input vector must be given initial

values. The following input and initial values were selected bO = -3.023 Cl = 56 X 10 ^"12 bl = 1.54 C2 = 150 X 10' ¹² b2 = -0.493 RO = 2100

Limitations were placed on the voltage sources to provide a circuit consistent with available input power, etc. Thus, -2.5 < VR and VRl < 10, and R0 > 0. Equation 8 above was used in a matrix having an entry for each of the following values:

An output vector is defined by minimizing the error of VRl, VR, FB, and RO in the matrix of equations. The output matrix is A = -0.177, 0.127, -1.52, 1.206*10 ⁴ . Thus, the circuit component values are VRl = -0.177, VR = 0.127, FB = -1.52, and RO = 1.206*10 ⁴ .

To determine the accuracy of the model, calculated enthalpy values are compared to actual enthalpy values. This was done for a temperature range of 55°F to 105°F, in 15° steps, and for relative humidity values from 0% to 100%, in 10% steps, and the error was generally less than 0.5 BTU/lb over the range of interest. Accordingly, it may be seen that the circuit above accurately calculates enthalpy.

Of course, the precise component values above must be implemented with commercially available resistors.

For the amplifier resistors commercially available resistorsRF = 16.2K and RI = 107K were selected.

Using these values in a mathcad program and solving for a 1% value of R0 gives the following results:

Cl = 56 PFD FB = -.1514

C2 = 150 PFD VRl = -.126 volts

R0 = 14,300Ω VR = +0.96 volts

Accordingly, the circuit in the embodiment of Figure 4 is implemented using these results. As one skilled in the art will readily know, other embodiments may use completely different values, or have values substantially as those given, but not exact (+/- 10% e.g.) . A similar routine was performed for the circuit of Figure 1 to determine the component values given above in the description of Figure 1.

In one embodiment of the invention enthalpy calculator 400 or 200 is part of a heating or cooling (i.e. environmental parameter control) system and after the enthalpy based on the sensed temperature and sensed

humidity is calculated, the value is transmitted to a control circuit (not shown) . The transmission may be over a wire or using an RF transmitter or similar device. In this way, the enthalpy value may be provided to a remote location to be used with other data in order to control a damper.

The position of the outside air damper controls how much outside air (external air) is delivered to the room or building being heated or cooled. The return air damper likewise controls the amount of heated or cooled air (energy controlled air) being recirculated in the room or building.

The controller which receives the calculated enthalpy value will adjust a damper to either utilize more or less "free air" depending upon the desired cooling, temperature of the room to be cooled, and the enthalpy of the "free air" relative to the controlled air, as is known to do so in the prior art. Accordingly, in one aspect of the invention, an air conditioning and/or heating system utilizes the enthalpy calculator disclosed herein to more economically cool and/or heat a room or building.

Although the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and broad scope of the appended claims.