RATIO MEMRISTORS

BACKGROUND

[0001] A memory system may be used to store data. In some examples, imaging devices, such as printheads may include memory to store information relating to printer cartridge identification, security information, and authentication information, among other types of information.

BRIEF DESCRIPTION OF THE DRAWINGS

[0002] The accompanying drawings illustrate various examples of the principles described herein and are a part of the specification. The illustrated examples do not limit the scope of the claims.

[0003] Fig. 1 is a diagram of a printing system according to one example of the principles described herein.

[0004] Fig. 2A is a diagram of a printer cartridge with a number of high resistance ratio memristors according to one example of the principles described herein.

[0005] Fig. 2B is a cross sectional diagram of a printer cartridge with a number of high resistance ratio memristors according to one example of the principles described herein.

[0006] Fig. 3 is a block diagram of a printer cartridge that uses a printhead with a number of high resistance ratio memristors according to one example of the principles described herein. [0007] Fig. 4 is a block diagram of a printhead with a number of high resistance ratio memristors according to one example of the principles described herein.

[0008] Fig. 5 is a block diagram of a printhead with a number of high resistance ratio memristors according to another example of the principles described herein.

[0009] Fig. 6 is a circuit diagram of a high resistance ratio memristor according to one example of the principles described herein.

[0010] Throughout the drawings, identical reference numbers designate similar, but not necessarily identical, elements.

DETAILED DESCRIPTION

[0011] Memory devices are used to store information for a printer cartridge. Printer cartridges include memory to store information related to the operation of the printhead. For example, a printhead may include memory to store information related 1) to the printhead; 2) to fluid, such as ink, used by the printhead; or 3) to the use and maintenance of the printhead. Other examples of information that may be stored on a printhead include information relating to 1) a fluid supply, 2) fluid identification information, 3) fluid characterization information, and 4) fluid usage data, among other types of fluid or imaging device related data. More examples of information that may be stored include identification information, serial numbers, security information, feature information, Anti-Counterfeiting (ACF) information, among other types of information. While memory usage on printheads is desirable, changing circumstances may reduce their efficacy in storing information.

[0012] For example, an increasing trend in counterfeiting may lead to current memory devices being too small to contain sufficient anti-counterfeiting information and security and authentication information. Additionally, with loyalty customer reward programs, new business models and other customer relation management programs through cloud-printing and other printing architectures, additional market data, customer appreciation value information, encryption information, and other types of information on the rise, a

manufacturer may desire to store more information on a memory device.

[0013] Moreover, as new technologies develop, circuit space becomes more valuable. Accordingly, it may be desirable for the greater amounts of data storage to occupy less space within a device. Memristors may be used due to their non-volatility, low operational power consumption characteristics, persistent data retention, and their compact size. A memristor selectively stores data based on a resistance state of the memristor. For example, a memristor may be in a low resistance state indicated by a "1 ," or a high resistance state indicated by a "0." Memristors may form a string of ones and zeroes that will store the aforementioned data. If an analog memristor is used, there may be many different resistance states.

[0014] A memristor may switch between a low resistance state and a high resistance state during a switching event in which a voltage is set across the memristor. Each memristor has a switching voltage that refers to a voltage used to switch the state of the memristors. When the supplied voltage is greater than the memristor switching voltage, the memristor switches state. The switching voltage is largely based on the size, thickness, and material composition of the memristor. For example, a thicker memristor may use a larger voltage to execute a switching event. While memristors may be beneficial as memory storage devices, their use presents a number of complications.

[0015] For example, memristors, along with other rewriteable memory elements, may be susceptible to hijacking as counterfeiters may alter the state of the memory elements to write new information to a memory array. So doing may compromise the security of the information as well as the ability of a manufacture to control its memory products.

[0016] Accordingly, the present specification describes a printhead and printer cartridge having high resistance ratio memristors. A resistance ratio refers to a ratio of the resistance of a memristor in a high resistance state (off) compared to the resistance of the memristor in a low resistance state (on). For example, a ratio of 3.5 may indicate that the memristor has a resistance in a high resistance state that is 3.5 times greater than the resistance of the memristor while in a low resistance state. Accordingly, as used in the present specification and in the appended claims, the term "high ratio" may refer to a ratio that is greater than or equal to 1000.

[0017] Specifically, high ratio memristors, when coupled to a voltage divider, may be such that once a memristor is programmed to a particular state, it cannot be re-written. For example, to set a memristor to a logic value of 1 , the memristor may be "set" from a virgin high resistance state to a low resistance state. By applying a sufficiently high forming voltage and allowing a large amount of current to flow during formation, the memristor may be set to a very low resistance state. Then during operation, use of a voltage divider, such as a resistor, disallows any supplied voltage (by a counterfeiter for example) from initiating a switching event such that the memristor may be "reset" from the very low resistance state to a high resistance state.

[0018] In some examples, a bi-polar memristor may be used. In this example, a first supplied voltage is used to "set" the memristor to a low resistance state and a second supplied voltage is used to "reset" the memristor to a high resistance state, the second supplied voltage being an opposite polarity relative to the first supplied voltage. However, as described above, using a voltage divider and a high resistance ratio memristor may disallow any second supplied voltage from "resetting" the bi-polar memristor.

[0019] More specifically, the present disclosure describes a printhead with a number of high resistance ratio memristors. The printhead includes a number of nozzles to deposit an amount of fluid onto a print medium. Each nozzle includes a firing chamber to hold the amount of fluid, an opening to dispense the amount of fluid onto the print medium, and an ejector to eject the amount of fluid through the opening. The printhead also includes a number of memristor banks connected in parallel. At least one of the number of memristor banks includes a number of high resistance ratio memristors. The printhead also includes a number of resistors disposed between a controller of a printer and the number of memristor banks to regulate the voltage to the number of memristor banks. [0020] The present disclosure describes a printer cartridge with a number of high resistance ratio memristors. The printer cartridge includes a fluid supply and a printhead to deposit fluid from the fluid supply onto a print medium. The printhead includes a number of high resistance ratio memristors having at least a low resistance state and a high resistance state and a number of resistors disposed between a controller on a printer and the number of high ratio memristors to regulate the voltage to the number of high resistance ratio memristors.

[0021] A printer cartridge and a printhead that utilize high resistance ratio memristors and a voltage dividing resistor may be beneficial by increasing the security of data and reducing the susceptibility of the memristor array to hijacking as the memristor is placed in a non-rewriteable state during formation and the voltage divider prevents the passing of a supplied voltage greater than the switching voltage of the memristor.

[0022] As used in the present specification and in the appended claims, the term "printer cartridge" may refer to a device used in the ejection of ink, or other fluid, onto a print medium. In general, a printer cartridge may be a fluidic ejection device that dispenses fluid such as ink, wax, polymers or other fluids. A printer cartridge may include a printhead. In some examples, a printhead may be used in printers, graphic plotters, copiers and facsimile machines. In these examples, a printhead may eject ink, or another fluid, onto a medium such as paper to form a desired image or a desired three-dimensional geometry.

[0023] Accordingly, as used in the present specification and in the appended claims, the term "printer" is meant to be understood broadly as any device capable of selectively placing a fluid onto a print medium. In one example the printer is an inkjet printer. In another example, the printer is a three-dimensional printer. In yet another example, the printer is a digital titration device.

[0024] Further, as used in the present specification and in the appended claims, the term "fluid" is meant to be understood broadly as any substance that continually deforms under an applied shear stress. In one example, a fluid may be a pharmaceutical. In another example, the fluid may be an ink. In another example, the fluid may be a liquid.

[0025] Still further, as used in the present specification and in the appended claims, the term "print medium" is meant to be understood broadly as any surface onto which a fluid ejected from a nozzle of a printer cartridge may be deposited. In one example, the print medium may be paper. In another example, the print medium may be an edible substrate. In yet one more example, the print medium may be a medicinal pill.

[0026] Still, as used in the present specification and in the appended claims, the term "memristor" may refer to a passive two-terminal circuit element that maintains a functional relationship between the time integral of current, and the time integral of voltage.

[0027] Still further, as used in the present specification and in the appended claims, the term "forming voltage" may refer to the voltage that initially puts the memristor in a low resistance state. The forming voltage may be applied to a virgin memristor, a virgin memristor being a memristor that has not yet been read from or written to.

[0028] Still further, as used in the present specification and in the appended claims, the term "switching voltage" may refer to the voltage that switches a memristor from a high resistance state to a low resistance state, from a low resistance state to a high resistance state, or combinations thereof after a memristor has been formed. As described above, using bi-polar memristors the switching voltage to "set" the memristor may be a first polarity and the switching voltage to "reset" the memristors may be a second, and opposite, polarity.

[0029] Still further, as used in the present specification and in the appended claims, the term "supplied voltage" may refer to a voltage supplied by a component to switch a memristor from a high resistance state to a low resistance state, from a low resistance state to a high resistance state, or combinations thereof. As described above, using bi-polar memristors the supplied voltage to "set" the memristor may be a first polarity and the supplied voltage to "reset" the memristors may be a second, and opposite, polarity. [0030] Yet further, as used in the present specification and in the appended claims, the term "resistance ratio" may refer to a ratio of the resistance of a memristor in a high resistance state compared to the resistance of the memristor in a low resistance state. For example, a resistance ratio of 3.5 may indicate that the memristor has a resistance in a high resistance state that is 3.5 times greater than the resistance of the memristor while in a low resistance state. Accordingly, as used in the present specification and in the appended claims, the term "high resistance ratio" may refer to a resistance ratio that is greater than or equal to 1 ,000.

[0031] Yet further, as used in the present specification and in the appended claims, the term "a number of" or similar language may include any positive number including 1 to infinity; zero not being a number, but the absence of a number.

[0032] In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present systems and methods. It will be apparent, however, to one skilled in the art that the present apparatus, systems, and methods may be practiced without these specific details. Reference in the specification to "an example" or similar language means that a particular feature, structure, or characteristic described is included in at least that one example, but not necessarily in other examples.

[0033] Turning now to the figures, Fig. 1 is a diagram of a printing system (100) according to one example of the principles described herein. In some examples, the printing system (100) is included on a printer. The system (100) includes an interface with a computing device (102). The interface enables the system (100), and specifically the processor (108), to interface with various hardware elements, such as the computing device (102), external and internal to the system (100). Other examples of external devices include external storage devices, network devices such as servers, switches, routers, and client devices among other types of external devices.

[0034] In general, the computing device (102) may be any source from which the system (100) may receive data describing a job to be executed by the controller (106) in order to eject fluid onto the print medium (126). For example, via the interface, the controller (106) receives data from the computing device (102) and temporarily stores the data in the data storage device (1 10). Data may be sent to the controller (106) along an electronic, infrared, optical, or other information transfer path. The data may represent a document and/or file to be printed. As such, data forms a job for the system (100) and includes job commands and/or command parameters.

[0035] A controller (106) includes a processor (108), a data storage device (1 10), and other electronics for communicating with and controlling the printhead (116). The controller (106) receives data from the computing device (102) and temporarily stores data in the data storage device (110).

[0036] The controller (106) controls the printhead (1 16) in ejecting fluid from the nozzles (124). For example, the controller (106) defines a pattern of ejected fluid drops that form characters, symbols, and/or other graphics or images on the print medium (126). The pattern of ejected fluid drops is determined by the print job commands and/or command parameters received from the computing device (102). The controller (106) may be an application specific integrated circuit (ASIC), on a printer for example, which determines the level of fluid in the printhead (116) based on resistance values of memristors integrated on the printhead (116). The ASIC may include a current source and an analog to digital converter (ADC). The ASIC converts a voltage present at the current source to determine a resistance of a memristor, and then determine a corresponding digital resistance value through the ADC. Computer readable program code, executed through executable instructions enables the resistance determination and the subsequent digital conversion through the ADC.

[0037] The processor (108) may include the hardware architecture to retrieve executable code from the data storage device (110) and execute the executable code. The executable code may, when executed by the processor (108), cause the processor (108) to implement at least the functionality of ejecting fluid onto the print medium (126). The executable code may, when executed by the processor (108), cause the processor (108) to implement the functionality of providing instructions to the power supply (130) such that the power supply (130) provides power to the components of the system (100).

[0038] The data storage device (1 10) may store data such as executable program code that is executed by the processor (108) or other processing device. The data storage device (110) may specifically store computer code representing a number of applications that the processor (108) executes to implement at least the functionality described herein.

[0039] Generally, the data storage device (110) may include a computer readable medium, a computer readable storage medium, or a non- transitory computer readable medium, among others. For example, the data storage device (110) may be an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of the computer readable storage medium may include, for example, the following: an electrical connection having a number of wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store computer usable program code for use by or in connection with an instruction execution system, apparatus, or device. In another example, a computer readable storage medium may be any non-transitory medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.

[0040] The printing system (100) includes a printer cartridge (114) that includes a printhead (1 16) and a reservoir (1 12). The printer cartridge (1 14) may be removable from the printer for example, as a replaceable printer cartridge (114).

[0041] The printer cartridge (1 14) includes a printhead (1 16) that ejects drops of fluid through a plurality of nozzles (124) towards a print medium (126). The print medium (126) may be any type of suitable sheet or roll material, such as paper, card stock, transparencies, polyester, plywood, foam board, fabric, canvas, and the like. In another example, the print medium (126) may be an edible substrate. In yet one more example, the print medium (126) may be a medicinal pill. As will be described below, the printhead (1 16) may include a number of high resistance ratio memristors and a voltage divider such that the memristors become non-rewriteable.

[0042] Nozzles (124) may be arranged in columns or arrays such that properly sequenced ejection of fluid from the nozzles (124) causes characters, symbols, and/or other graphics or images to be printed on the print medium (126) as the printhead (1 16) and print medium (126) are moved relative to each other. In one example, the number of nozzles (124) fired may be a number less than the total number of nozzles (124) available and defined on the printhead (1 16).

[0043] The printer cartridge (1 14) also includes a fluid reservoir (112) to supply an amount of fluid to the printhead (116). In general, fluid flows between the reservoir (112) and the printhead (116). In some examples, a portion of the fluid supplied to printhead (1 16) is consumed during operation and fluid not consumed during printing is returned to the reservoir (112).

[0044] In some examples, a mounting assembly positions the printhead (116) relative to a media transport assembly, and media transport assembly positioning the print medium (126) relative to the printhead (1 16). Thus, a print zone (128), indicated by the dashed box, is defined adjacent to the nozzles (124) in an area between the printhead (116) and the print medium (126). In one example, the printhead (1 16) is a scanning type printhead (116). As such, the mounting assembly includes a carriage for moving the printhead (1 16) relative to the media transport assembly to scan the print medium (126). In another example, the printhead (116) is a non-scanning type printhead (1 16). As such, the mounting assembly fixes the printhead (116) at a prescribed position relative to the media transport assembly. Thus, the media transport assembly positions the print medium (126) relative to the printhead (116).

[0045] Fig. 2A is a diagram of a printer cartridge (114) and printhead (1 16) with a number of high resistance ratio memristors according to one example of the principles described herein. As discussed above, the printhead (1 16) may include a number of nozzles (124). In some examples, the printhead (1 16) may be broken up into a number of print dies with each die having a number of nozzles (124). The printhead (116) may be any type of printhead (1 16) including, for example, a printhead (1 16) as described in Figs. 2A and 2B. The examples shown in Figs. 2A and 2B are not meant to limit the present description. Instead, various types of printheads (1 16) may be used in conjunction with the principles described herein.

[0046] The printer cartridge (1 14) also includes a fluid reservoir (112), a flexible cable (236), conductive pads (238), and a memristor array (240). The flexible cable (236) is adhered to two sides of the printer cartridge (1 14) and contains traces that electrically connect the memristor array (240) and printhead (1 16) with the conductive pads (238).

[0047] The printer cartridge (114) may be installed into a cradle. When the printer cartridge (114) is correctly installed into a device such as a printer, the conductive pads (238) are pressed against corresponding electrical contacts in the cradle, allowing the device to communicate with, and control the electrical functions of, the printer cartridge (1 14). For example, the conductive pads (238) allow the device to access and write to the memristor array (240).

[0048] The memristor array (240) may store a variety of information including the type of printer cartridge (114), the kind of fluid contained in the printer cartridge (1 14), an estimate of the amount of fluid remaining in the fluid reservoir (1 12), calibration data, error information, and other data. In one example, the memristor array (240) may include information regarding when the printer cartridge (1 14) should be maintained. The memristor array (240) may include other information as described below in connection with Fig. 3. As will be described below the memristor array (240) may include a number of non- rewriteable memristors being formed of memristors with high resistance ratios and voltage dividers.

[0049] To eject fluid, the system (Fig. 1 , 100) moves the carriage containing the printer cartridge (114) relative to a print medium (Fig. 1 , 126). At appropriate times, the system (Fig. 1 , 100) sends electrical signals to the printer cartridge (1 14) via the electrical contacts in the cradle. The electrical signals pass through the conductive pads (238) and are routed through the flexible cable (236) to the printhead (116). The printhead (116) then ejects a small droplet of fluid from the reservoir (1 12) onto the surface of the print medium (Fig. 1 , 126).

[0050] The printhead (116) may include any number of nozzles (124). In an example where the fluid is an ink, a first subset of nozzles (124) may eject a first color of ink while a second subset of nozzles (124) may eject a second color of ink. Additional groups of nozzles (124) may be reserved for additional colors of ink.

[0051] Fig. 2B is a cross sectional diagram of a printer cartridge (114) and printhead (116) with a number of high resistance ratio memristors according to one example of the principles described herein. The printer cartridge (114) may include a fluid supply (112) that supplies the fluid to the printhead (116) for deposition onto a print medium. In some examples, the fluid may be ink. For example, the printer cartridge (1 14) may be an inkjet printer cartridge, the printhead (116) may be an inkjet printhead, and the ink may be inkjet ink.

[0052] The printer cartridge (114) may include a printhead (116) to carry out at least a part of the functionality of depositing fluid onto a print medium (Fig. 1 , 126). The printhead (116) may include a number of

components for depositing a fluid onto a print medium (Fig. 1 , 126). For example, the printhead (116) may include a number of nozzles (124). For simplicity, Fig. 2B indicates a single nozzle (124); however a number of nozzles (124) are present on the printhead (1 16). A nozzle (124) may include an ejector (242), a firing chamber (244), and an opening (246). The opening (246) may allow fluid, such as ink, to be deposited onto a surface, such as a print medium (Fig. 1 , 126). The firing chamber (244) may include a small amount of fluid. The ejector (242) may be a mechanism for ejecting fluid through an opening (246) from a firing chamber (244), where the ejector (242) may include a firing resistor or other thermal device, a piezoelectric element, or other mechanism for ejecting fluid from the firing chamber (244). [0053] For example, the ejector (242) may be a firing resistor. The firing resistor heats up in response to an applied voltage. As the firing resistor heats up, a portion of the fluid in the firing chamber (244) vaporizes to form a bubble. This bubble pushes liquid fluid out the opening (246) and onto the print medium (Fig. 1 , 126). As the vaporized fluid bubble pops, a vacuum pressure within the firing chamber (244) draws fluid into the firing chamber (244) from the fluid supply (1 12), and the process repeats. In this example, the printhead (1 16) may be a thermal inkjet printhead.

[0054] In another example, the ejector (242) may be a piezoelectric device. As a voltage is applied, the piezoelectric device changes shape which generates a pressure pulse in the firing chamber (244) that pushes a fluid out the opening (246) and onto the print medium (Fig. 1 , 126). In this example, the printhead (116) may be a piezoelectric inkjet printhead.

[0055] The printhead (116) and printer cartridge (114) may also include other components to carry out various functions related to fluidic ejection. For simplicity, in Figs. 2A and 2B, a number of these components and circuitry included in the printhead (116) and printer cartridge (114) are not indicated; however such components may be present in the printhead (116) and printer cartridge (1 14). In some examples, the printer cartridge (114) is removable from a printing system for example, as a disposable printer cartridge.

[0056] Fig. 3 is a block diagram of a printer cartridge (114) that uses a printhead (116) with a number of high resistance ratio memristors according to one example of the principles described herein. In some examples, the printer cartridge (1 14) includes a printhead (1 16) that carries out at least a part of the functionality of the printer cartridge (1 14). For example, the printhead (1 16) may include a number of nozzles (Fig. 1 , 124). The printhead (1 16) ejects drops of fluid from the nozzles (Fig. 1 , 124) onto a print medium (Fig. 1 , 126) in accordance with a received print job. The printhead (116) may also include other circuitry to carry out various functions related to printing. In some examples, the printhead (1 16) is part of a larger system such as an integrated printhead (I PH). The printhead (1 16) may be of varying types. For example, the printhead (116) may be a thermal inkjet (TIJ) printhead or a piezoelectric inkjet (PIJ) printhead, among other types of printhead (1 16).

[0057] The printhead (116) includes a memristor array (240) to store information relating to at least one of the printer cartridge (114) and the printhead (116). In some examples, the memristor array (240) includes a number of memristor banks (348). Each memristor bank (348) may include a number of high resistance ratio memristors fabricated into the printhead (116). To store information, a memristor within each memristor bank (348) may be set to a particular resistance state. As memristors are non-volatile, this resistance state is retained even when power is removed from the printhead (116).

[0058] A memristor has a metal-insulator-metal layered structure. More specifically, the memristor may include a bottom electrode (metal), a switching oxide (insulator), and a top electrode (metal). A memristor may be classified as an anion device which includes an n-type oxide insulator where the dominant migration species are oxygen ions. Examples of such oxide insulators include transition metal oxides, complex oxides, and large band gap dielectrics in addition to other non-oxide materials. In this example, an aluminum oxide, silicon oxide, or tantalum oxide may examples anionic oxide memristors. In an anionic device, the switching mechanism may be the formation of conductive channels in the switching oxide due to the migration of positively charged oxygen vacancies in the oxide. By comparison, in a cationic device which includes a p-type oxide insulator; a conductive channel is formed from cationic species such as copper or silver ions which are electrochemically active. A memristor may operate with either anionic or cationic mechanisms.

[0059] The number of memristor banks (348) are grouped together into a memristor array (240). In some examples, the memristor bank (348) may have a cross bar structure. In this example, each memristor may be formed at an intersection of a first set of elements and a second set of elements, the elements forming a grid of intersecting nodes, each node defining a memristor. In another example, the memristor array (240) may include a number of memristor banks (348-1 , 348-2), in which the memristors in those memristor banks (348) form a one-to-one structure with a number of transistors. For example, an integrated circuit may include a number of addressing units. Each addressing unit may include a number of components that allow for multiplexing and logic operations. The memristor may be designed to be individually addressed by a distinct addressing unit. In some examples, the addressing units may be transistors. In this example, the memristor may share a one transistor-one memristor (1T1 M) addressing structure with the addressing units of the integrated circuit.

[0060] The memristor array (240) may be used to store any type of data. Examples of data that may be stored in the memristor array (240) include fluid supply specific data and/or fluid identification data, fluid characterization data, fluid usage data, printhead (116) specific data, printhead (116) identification data, warranty data, printhead (116) characterization data, printhead (116) usage data, authentication data, security data, Anti- Counterfeiting data (ACF), fluid drop weight, firing frequency, initial printing position, acceleration information, and gyro information, among other forms of data. In a number of examples, the memristor array (240) is written at the time of manufacturing and/or during the operation of the printer cartridge (114).

[0061] In some examples, the printer cartridge (1 14) may be coupled to a controller (106). The controller (106) receives a control signal from an external computing device (Fig. 1 , 102). The controller (106) may be an Application-Specific Integrated Circuit (ASIC), for example, a printer ASIC. A computing device (Fig. 1 , 102) may send a print job to the printer cartridge (1 14), the job being made up of text, images, or combinations thereof to be deposited onto a print medium (Fig. 1 , 126). The controller (106) may facilitate storing information to the memristor array (240). Specifically, the controller (106) may pass at least one control signal to the number of memristor banks (348). For example, the controller (106) may be coupled to the printhead (116), via an access line such as an identification line. Via the identification line, the controller (106) may change the resistance state of a number of memristors in the memristor array (240) to effectively store information to a memristor array (240). For example, the controller (106) may send data such as authentication data, security data, and job data, in addition to other types of data to the printhead (116) to be stored on the memristor array (240).

[0062] While specific reference is made to an access line, such as an ID line, the controller (106) may share a number of lines of communication with the printhead (116), such as data lines, clock lines, and fire lines. For simplicity, in Fig. 3 the different communication lines are indicated by a single arrow.

[0063] Fig. 4 is a block diagram of a printhead (1 16) with a number of high resistance ratio memristors according to one example of the principles described herein. As described above a printhead (116) may include a memristor array (240) that is divided into a number of memristor banks (348-1 , 348-2). The memristor banks (348) may be connected in parallel. At least one of the memristor banks (348) includes a number of high resistance ratio memristors. High resistance ratio memristors are those memristors whose ratio between a high resistance state (which indicates one logic value) and a low resistance state (which indicates another logic value) is greater than a certain amount. For example, a high resistance ratio memristor may have a high resistance state/low resistance state ratio, or "off/on" resistance ratio, of greater than 1 ,000. For example, a memristor may have a high resistance state of 1 ,000,000 Ohms (Ω) and a low resistance state of 1 ,000 Ω. In this example, the memristor may have a ratio of 1 ,000 (i.e., 1 ,000,000 Ω divided by 1 ,000 Ω). This memristor may be a high resistance ratio memristor. As will be described below, when used in connection with a voltage divider (450) a high resistance ratio memristor may be non-rewriteable. A high resistance ratio memristor may be in a permanently low resistance state, or "on" state, after formation and may not be "reset" to a high resistance state, or "off" state. As will be describe below, the permanently low resistance state of the memristor may be provided by the high resistance ratio of the memristor in conjunction with the voltage divider resistor.

[0064] As depicted in Fig. 4, a memristor array (240) may have multiple memristor banks (348) with at least one having a number of high resistance ratio memristors. The other memristor bank (348) may also have a number of high resistance ratio memristors or may have a number of standard resistance ratio memristors. Having both high resistance ratio memristors and standard resistance ratio memristors in a memristor array (240) may be beneficial by allowing certain portions, or certain data, to be write-protected while allowing other portions of the memristor array (240) to be rewriteable. Doing so may increase the flexibility of data storage in a memristor array (240), such as a memristor array (240) on a printhead (1 16).

[0065] A high resistance ratio memristor may be hard-formed by passing a supplied voltage to the memristor that is significantly higher than the forming voltage of the memristor. For example, a memristor may have a forming voltage of 2-3 volts (V). A supplied voltage of between 10 V and 15 V may be passed through the memristor during formation of the memristor. At the same time a large current may be passed to the memristor during formation. For example, a current of approximately 1 to 10 milliAmperes (mA) may be passed to the memristor during formation. While specific values of voltages and current are presented any voltage and current may be used such that the memristor is hard-formed.

[0066] Passing a large current may include raising the current compliance level for the printhead (116). A current compliance level may refer to a maximum current allowed by a hardware or circuit and may be a protection against hardware and over-forming a memristor. Accordingly, in order to pass a large current such as 1-10 mA, the current compliance level may be raised such that the supplied current of 1-10 mA may be passed to the memristor. By increasing the current compliance level and increasing the supplied current to a memristor during formation, a memristor may be formed with increased conductive filaments in the switching oxide. The increased conductive filaments increase the conductivity of the memristor and thereby reduce the resistance to electrical current. In other words, applying a large current during formation of the memristor results in a memristor that has a very low resistance, such as less than 100 Ω. As an initial resistance of the memristor may be much larger, increasing the current compliance level of a memristor and passing a large current through the memristor yields a high resistance ratio memristor. [0067] While a specific example has been given using specific values, any value of voltage and current may be used to form the high resistance ratio memristors. In fact, the value of the voltage, current, and initial high resistance state of the memristor may be manipulated to generate any desired ratio memristor. For example, the first memristor bank (348-1) may include a first number of high resistance ratio memristors with a first ratio. The second memristor bank (348-2) may include a second number of high resistance ratio memristors with a second ratio, the second ratio being distinct from the first ratio. Allowing memristors with different resistance ratios may be beneficial by offering another degree of flexibility in designing a memristor array (240).

[0068] The printhead (116) may also include a voltage divider (450) to reduce the voltage to the number of memristor banks (348). More specifically, the voltage divider (450) may reduce the voltage that is seen by the high resistance ratio memristors after formation. The voltage divider (450) may have the effect of reducing the voltage seen by the memristor. Due to the low resistance of the high resistance ratio memristor and the voltage divider, the memristor is non-rewriteable. In other words, the memristor has a large switching voltage such that it is greater than a supplied voltage from the controller (106). An example is given as follows. In this example, the voltage divider (450) may be a resistor with a value of approximately 20,000 Ω ( ¾,-„), the initial high resistance state of the memristor is 1 ,000,000 Ω (Rhmem) and a forming voltage ( _orm ) of 15 V is applied across the memristor. In this example, the memristor has a forming voltage of 3 V. According to the voltage divider rule, the voltage seen by the memristor ( V _mem ) during a "set" operation can be evaluated according to Equation 1 below:

Vmem = _(R form Equation (1).

[0069] Based on Equation (1), V _mem is 14.7 V. Equation (1) applies to both a uni-polar memristor and a bi-polar memristor. As this is greater than the switching voltage (3 V) of the memristor, the memristor is switched to a very low resistance state, such as 100 Ω, which low resistance state is determined based on the voltage supplied during formation as well as the current supplied to the memristor during formation. Using the after-formation low resistance (Rimem) of the memristor, the voltage seen by the memristor (V _mem ) during a "reset" operation may be evaluated according to Equation (2) below:

Vmem = _(R form Equation (2).

[0070] For a uni-polar memristor, based on Equation (2) V _mem \s .07 V. Using Equation (2), the voltage seen by a bi-polar memristor V _mem during a "reset" operation may be evaluated by changing the \/ _form to have an opposite polarity, for example -15 V. In this example, based on Equation (2), V _mem ^' is - .07 V for a bi-polar memristor. In either case, this is less than the switching voltage (3 V) of the memristor, and accordingly the memristor is not switched to a high resistance state. Accordingly, the voltage divider as well as the high resistance ratio memristor forms a memristor that is non-rewriteable after formation.

[0071] The voltage divider (450) may be a resistor disposed between the controller (106) that is disposed on a printer and the number of memristor banks (348). In some examples, the voltage divider (450) may be placed on the access line (552). In this example, a single voltage divider (450) may be used for the number of memristor banks (348). While specific reference has been made to a voltage divider (450) resistor with a fixed resistance, the voltage divider (450) resistor may be a dynamic resistor such as a dynamic metal-oxide semiconductor field effect transistor (MOSFET).

[0072] Fig. 5 is a block diagram of a printhead (1 16) with a number of high resistance ratio memristors according to another example of the principles described herein. In this example, the memristor array (240) may include multiple voltage dividers (450-1 , 450-2), each voltage divider (450) associated with a particular memristor bank (348). For example, a first voltage divider (450-1) may correspond to a first memristor bank (348-1) and a second voltage divider (450-2) may correspond to a second memristor bank (348-2). As the voltage dividers (450) may be resistors, each memory bank (348) may have an independently paired resistor. In some examples, the resistors may have different resistance values. For example, a first resistor may have a resistance of 20,000 Ω and a second resistor may have a resistance of 10,000 Ω. Again, while specific reference is made to fixed value resistors, the voltage dividing resistors may be dynamic resistance resistors. Implementing resistors with different resistances may be beneficial as the rewriteable characteristics may be tuned as desired. In addition to having a voltage divider (450) per memristor bank (348), the voltage divider (450) such as a resistor may be serially connected to the corresponding memristor bank (348).

[0073] Fig. 6 is a circuit diagram of a high resistance ratio memristor (654) according to one example of the principles described herein. As described above, a memristor (654) is a memory element that stores

information based on a resistance state of the memristor (654), a high resistance state indicating one logic value and a low resistance state indicating another logic value. A high resistance ratio memristor (654) may be a memristor with a ratio of a high resistance state to a low resistance state that is greater than a threshold amount, for example 1 ,000. The high resistance ratio memristor (654) may be formed by applying a supplied voltage that is greater than a forming voltage of the memristor (for example, 1.2 times greater than the forming voltage) and by supplying a large current, on the order of 1-10 mA, to the memristor (654). Applying a large voltage and a large current places the memristor (654) in a very low resistance state (on the order of 100 Ω), such that any subsequently supplied voltage will not be greater than the switching voltage of the memristor (654). To this end, a voltage divider (Fig. 4, 450) such as a resistor (656), which may be static or dynamic, may be coupled to the memristor (654). As described in connection with Fig. 3, the resistor (656) or number of resistors (656) may be along an access line (Fig. 5, 552) connecting the printhead (Fig. 1 , 1 16) to a controller (106) in the system (Fig. 1 , 100). In another example, the resistors (656) may be coupled serially to each memristor (654) or memristor bank (Fig. 3, 348). While Fig. 6 depicts a resistor (656) coupled to a single memristor (654), the resistor (656) may be coupled to any number of memristors (654) for example to a number of memristors (654) in a memristor bank (Fig. 3, 348). As depicted in Fig. 6 and described herein, the resistor (656) acts as a voltage divider (Fig. 4, 450) to reduce the voltage applied across the memristor (654) such that a supplied voltage is not greater than the switching voltage of the memristor (654).

[0074] The memristor bank (Fig. 3, 348) may have a cross bar structure. In this example, each memristor (654) may be coupled to a first transistor (658-1) and a second transistor (658-2). In a cross bar structure a number of columns of traces and a number of rows of traces may be positioned to form a grid. Each intersection of the grid defines a memristor (654). A memristor (654) may be selected by actively selecting a row and a column. An active memristor (654) is a memristor (654) whose row and column are selected. In this example, a first transistor (658-1) may be used to indicate a row of the memristor (654) has been selected and a second transistor (658-2) may be used to indicate a column of the memristor (654) has been selected. Accordingly, a memristor (654) may be selected when both transistors (658-1 , 658-2) are closed. While Fig. 6 depicts a memristor (654) with two transistors (658) as in a cross bar structure, the memristor (654) may be used in a one-to- one relationship with a transistor such that a single transistor (658) may be used to select a particular memristor (654). While Fig. 6 depicts the memristor (654) being above two cascading transistors (658) other orientations may also be used. For example, the memristor (654) may be below two cascading transistors (658), or may be between two transistors (658).

[0075] A transistor (658) is a device that regulates current and acts as a switch for electronic signals. For example, a transistor (658) may allow current to flow through the memristor (654), which flow changes a state of the memristor (654), i.e., from a low resistance state to a high resistance state or from a high resistance state to a low resistance state. As described above, this change of state allows a memristor (654) to store information. A transistor (658) may include a source, a gate, and a drain. Electrical current flows from the source to the drain based on an applied voltage at the gate. For example, when no voltage is applied at the gate, no current flows between the source and the drain. By comparison, when there is an applied voltage at the gate, current readily flows between the source and the drain.

[0076] A printer cartridge (Fig. 1 , 114) and printhead (Fig. 1 , 1 16) with a number of high resistance ratio memristors (654) may have a number of advantages, including: (1) reducing the resistance of a memristor (654) such that a supplied voltage does not inadvertently or maliciously switch the state of the memristor (654); (2) provide a non-rewriteable memristor array (Fig. 2, 240); (3) allow selection of operating parameters of the memristor array (Fig. 2, 240); and (4) improving printhead (Fig. 1 , 116) memory performance.

[0077] Aspects of the present system are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to examples of the principles described herein. Each block of the flowchart illustrations and block diagrams, and combinations of blocks in the flowchart illustrations and block diagrams, may be implemented by computer usable program code. The computer usable program code may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the computer usable program code, when executed via, for example, the processor (Fig. 1 , 108) of the system (Fig. 1 , 100) or other programmable data processing apparatus, implement the functions or acts specified in the flowchart and/or block diagram block or blocks. In one example, the computer usable program code may be embodied within a computer readable storage medium; the computer readable storage medium being part of the computer program product. In one example, the computer readable storage medium is a non-transitory computer readable medium.

[0078] The preceding description has been presented to illustrate and describe examples of the principles described. This description is not intended to be exhaustive or to limit these principles to any precise form disclosed. Many modifications and variations are possible in light of the above teaching.