HIGHLY LINEAR MULTIPLIER

Abstract

There is provided a linearized multiplier configured to produce an output current representing a product of a first input voltage and a second input voltage, comprising: a first transconductance stage which is configured to input the first input voltage and to output a first pair of differential currents, wherein the first transconductance stage comprises a negative feedback network, at least one second transconductance stage which is configured to input the second input voltage and to output a pre-distorted voltage of the second input voltage, wherein each second transconductance stage comprises a negative feedback network, a pair of third transconductance stages, each of which is configured to input a voltage corresponding to the pre-distorted voltage of the second input voltage and to output a second pair of differential currents, when being supplied with a bias current corresponding to a respective current of the first pair of differential currents.

Claims

1. A multiplier (1A, 1B, 1C) configured to produce an output current representing a product of a first input voltage and a second input voltage, comprising: a first transconductance stage which is configured to input the first input voltage and to output a first pair of differential currents, when being supplied with a first fixed bias current, wherein the first transconductance stage comprises a negative feedback network, at least one second transconductance stage which is configured to input the second input voltage and to output a pre-distorted voltage of the second input voltage, when being supplied with a second fixed bias current, wherein each second transconductance stage comprises a negative feedback network, a pair of third transconductance stages, each of which is configured to input a voltage corresponding to the pre-distorted voltage of the second input voltage and to output a second pair of differential currents, when being supplied with a bias current corresponding to a respective current of the first pair of differential currents, and a combination network which is configured to generate the output current by combining the second pairs of differential currents from both of the pair of third transconductance stages.

2. The multiplier according to claim 1, wherein the first transconductance stage comprises two current outputs for each of the first pair of differential currents, and the first transconductance stage is configured such that, for each of the first pair of differential currents, one of the two current outputs is subtracted from a first reference current corresponding to an output current at an operating point of the first transconductance stage and the resulting current difference is fed back via a feedback resistor to an input side of the first transconductance stage, and the other one of the two current outputs is output from the first transconductance stage.

3. The multiplier according to claim 2, wherein each second transconductance stage is configured such that, for each of a pair of currents at an output side of the second transconductance stage, the current is subtracted from a second reference current corresponding to an output current at an operating point of the second transconductance stage and the resulting current difference is fed back via a feedback resistor on a feedback path to an input side of the second transconductance stage, and each second transconductance stage is configured to output, as the pre-distorted voltage, a potential difference between the two feedback paths.

4. The multiplier according to claim 1, wherein the second fixed bias current of a second transconductance stage is set to be in the middle of a range of the bias current of a third transconductance stage which is configured to input the voltage based on the pre-distorted voltage from said second transconductance stage.

5. The multiplier according to claim 1, wherein a transconductance of a second transconductance stage is at least substantially equal to a transconductance of a third transconductance stage which is configured to input the voltage based on the pre-distorted voltage from said second transconductance stage.

6. The multiplier according to claim 1, wherein a second transconductance stage and a third transconductance stage which is configured to input the voltage based on the pre-distorted voltage from said second transconductance stage are matched to each other.

7. The multiplier according to claim 1, wherein a gain of a second transconductance stage is set to be such that input of the pre-distorted voltage of the second input voltage causes a third transconductance stage, which is configured to input the voltage based on the pre-distorted voltage from said second transconductance stage, to output the second pair of differential currents being equal to a pair of differential currents which is generated by the transconductance of said second transconductance stage upon input of the second input voltage.

8. The multiplier according to claim 1, wherein each third transconductance stage is configured to input the pre-distorted voltage of the second input voltage from a second transconductance stage.

9. The multiplier according to claim 1, further comprising: an error compensating circuit which is configured to generate a compensated voltage for compensating an error in the output current with respect to an exact algebraic product of the first input voltage and the second input voltage.

10. The multiplier according to claim 1, further comprising: at least one fourth transconductance stage which is configured to input the second input voltage and to output a scaled voltage of the second input voltage, when being supplied with a third fixed bias current, and at least one multiplication-addition network which is configured to generate a compensated voltage of the second input voltage by multiplying the pre-distorted voltage of the second input voltage from a second transconductance stage by a first factor, multiplying the scaled voltage of the second input voltage from a fourth transconductance stage by a second factor and adding the multiplied pre-distorted voltage and the multiplied scaled voltage, wherein each third transconductance stage is configured to input the compensated voltage of the second input voltage from a multiplication-addition network.

11. The multiplier according to claim 1, wherein each transconductance stage comprises a differential pair of CMOS transistors with the bias current as tail current.

12. The multiplier according to claim 1, wherein the multiplier is integrated in CMOS technology.

13. The multiplier according to claim 11, wherein the first transconductance stage is built with NMOS transistors, and any one of the second and third transconductance stages are built with PMOS transistors.

14. The multiplier according to claim 1, wherein the first and second input voltages are or represent analog signals, or at least one of the first and second input voltages is or represents a signal resulting from pulse width modulation of an analog signal, or one of the first and second input voltages is or represents a signal a reference signal of a digital-to-analog converter, and the other one of the first and second input voltages is or represents a digital input of the digital-to-analog converter.

15. A multiplier (1A, 1B, 1C) configured to produce an output current representing a product of a first input voltage and a second input voltage, comprising: a first transconductance stage which is configured to input the first input voltage and to output a first pair of differential currents, when being supplied with a first fixed bias current, wherein the first transconductance stage comprises a negative feedback network, at least one second transconductance stage which is configured to input the second input voltage and to output a pre-distorted voltage of the second input voltage, when being supplied with a second fixed bias current, wherein each second transconductance stage comprises a negative feedback network, a pair of third transconductance stages, each of which is configured to input a voltage corresponding to the pre-distorted voltage of the second input voltage and to output a second pair of differential currents, when being supplied with a bias current corresponding to a respective current of the first pair of differential currents, and a combination network which is configured to generate the output current by combining the second pairs of differential currents from both of the pair of third transconductance stages, wherein the first transconductance stage comprises two current outputs for each of the first pair of differential currents, the first transconductance stage is configured such that, for each of the first pair of differential currents, one of the two current outputs is subtracted from a first reference current corresponding to an output current at an operating point of the first transconductance stage and the resulting current difference is fed back via a feedback resistor to an input side of the first transconductance stage, and the other one of the two current outputs is output from the first transconductance stage, each second transconductance stage is configured such that, for each of a pair of currents at an output side of the second transconductance stage, the current is subtracted from a second reference current corresponding to an output current at an operating point of the second transconductance stage and the resulting current difference is fed back via a feedback resistor on a feedback path to an input side of the second transconductance stage, and each second transconductance stage is configured to output, as the pre-distorted voltage, a potential difference between the two feedback paths.

16. The multiplier according to claim 15, wherein the second fixed bias current of a second transconductance stage is set to be in the middle of a range of the bias current of a third transconductance stage which is configured to input the voltage based on the pre-distorted voltage from said second transconductance stage, a transconductance of a second transconductance stage is at least substantially equal to a transconductance of a third transconductance stage which is configured to input the voltage based on the pre-distorted voltage from said second transconductance stage, and a second transconductance stage and a third transconductance stage which is configured to input the voltage based on the pre-distorted voltage from said second transconductance stage are matched to each other.

17. The multiplier according to claim 15, wherein a gain of a second transconductance stage is set to be such that input of the pre-distorted voltage of the second input voltage causes a third transconductance stage, which is configured to input the voltage based on the pre-distorted voltage from said second transconductance stage, to output the second pair of differential currents being equal to a pair of differential currents which is generated by the transconductance of said second transconductance stage upon input of the second input voltage.

18. The multiplier according to claim 15, further comprising: at least one fourth transconductance stage which is configured to input the second input voltage and to output a scaled voltage of the second input voltage, when being supplied with a third fixed bias current, and at least one multiplication-addition network which is configured to generate a compensated voltage of the second input voltage by multiplying the pre-distorted voltage of the second input voltage from a second transconductance stage by a first factor, multiplying the scaled voltage of the second input voltage from a fourth transconductance stage by a second factor and adding the multiplied pre-distorted voltage and the multiplied scaled voltage, wherein each third transconductance stage is configured to input the compensated voltage of the second input voltage from a multiplication-addition network.

19. A multiplier (1A, 1B, 1C) configured to produce an output current representing a product of a first input voltage and a second input voltage, comprising: a first transconductance stage which is configured to input the first input voltage and to output a first pair of differential currents, when being supplied with a first fixed bias current, wherein the first transconductance stage comprises a negative feedback network, at least one second transconductance stage which is configured to input the second input voltage and to output a pre-distorted voltage of the second input voltage, when being supplied with a second fixed bias current, wherein each second transconductance stage comprises a negative feedback network, a pair of third transconductance stages, each of which is configured to input a voltage corresponding to the pre-distorted voltage of the second input voltage and to output a second pair of differential currents, when being supplied with a bias current corresponding to a respective current of the first pair of differential currents, and a combination network which is configured to generate the output current by combining the second pairs of differential currents from both of the pair of third transconductance stages, wherein each transconductance stage is realized with MOSFET transistors in CMOS technology.

20. The multiplier according to claim 19, wherein the first transconductance stage comprises two current outputs for each of the first pair of differential currents, the first transconductance stage is configured such that, for each of the first pair of differential currents, one of the two current outputs is subtracted from a first reference current corresponding to an output current at an operating point of the first transconductance stage and the resulting current difference is fed back via a feedback resistor to an input side of the first transconductance stage, and the other one of the two current outputs is output from the first transconductance stage, each second transconductance stage is configured such that, for each of a pair of currents at an output side of the second transconductance stage, the current is subtracted from a second reference current corresponding to an output current at an operating point of the second transconductance stage and the resulting current difference is fed back via a feedback resistor on a feedback path to an input side of the second transconductance stage, and each second transconductance stage is configured to output, as the pre-distorted voltage, a potential difference between the two feedback paths.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In the following, the present disclosure will be described in greater detail by way of non-limiting examples with reference to the accompanying drawings, in which

[0038] FIG. 1 shows an example of a circuit diagram of a differential stage of CMOS transistors, i.e. a CMOS differential pair,

[0039] FIG. 2 shows examples of characteristics of the differential stage shown in FIG. 1, wherein FIG. 2(a) shows an example of a voltage-current transfer function and FIG. 2(b) shows an example of a transconductance function,

[0040] FIG. 3 shows examples of further characteristics of the differential stage shown in FIG. 1, wherein FIG. 3(a) shows an example of a current-current transfer function and FIG. 3(b) shows an example of a function of the derivative of the current difference,

[0041] FIG. 4 shows an example of a circuit diagram of a multiplier according to an embodiment,

[0042] FIG. 5 shows an example of a circuit diagram of a voltage-input unit which is applicable in a multiplier according to an embodiment,

[0043] FIG. 6 shows an example of a circuit diagram of another voltage-input unit which is applicable in a multiplier according to an embodiment,

[0044] FIG. 7 shows another example of a circuit diagram of a multiplier according to an embodiment,

[0045] FIG. 8 shows an example of a modulation characteristic of the multiplier in line with the circuit diagram of FIG. 7 according to an embodiment,

[0046] FIG. 9 shows an example of an operating process or signal flow of the multiplier in line with the circuit diagram of FIG. 7 according to an embodiment,

[0047] FIG. 10 shows examples of transistor circuits of various parts of/for an multiplier according to an embodiment,

[0048] FIG. 11 shows an example of a modulation characteristic of the multiplier in line with the transistor circuits of FIG. 10 according to an embodiment,

[0049] FIG. 12 shows an example of a linearity characteristic of the multiplier in line with the transistor circuits of FIG. 10 according to an embodiment,

[0050] FIG. 13 shows examples of error characteristics with respect to a first input voltage of the multiplier in line with the circuit diagram of FIG. 7 according to an embodiment,

[0051] FIG. 14 shows examples of error characteristics with respect to a second input voltage of the multiplier in line with the circuit diagram of FIG. 7 according to an embodiment,

[0052] FIG. 15 shows still another example of a circuit diagram of a multiplier according to an embodiment,

[0053] FIG. 16 shows examples of error characteristics with respect to a first input voltage of the multiplier in line with the circuit diagram of FIG. 15 according to an embodiment,

[0054] FIG. 17 shows examples of error characteristics with respect to a second input voltage of the multiplier in line with the circuit diagram of FIG. 15 according to an embodiment, and

[0055] FIG. 18 shows an example of an operating process or signal flow of the multiplier in line with the circuit diagram of FIG. 15 according to an embodiment.

DETAILED DESCRIPTION

[0056] The present disclosure is described herein with reference to particular non-limiting examples and to what are presently considered to be conceivable (examples of) embodiments. A person skilled in the art will appreciate that the present disclosure is by no means limited to these examples and embodiments, and may be more broadly applied.

[0057] It is to be noted that the following description mainly refers to specifications being used as non-limiting examples and embodiments for certain exemplifying circuit structures, implementations and technologies. Such description is only used in the context of the presented non-limiting examples and embodiment, and does naturally not limit the present disclosure in any way. Rather, any other circuit structures, implementations and technologies may equally be utilized as long as complying with what is described herein and/or embodiments described herein are applicable thereto.

[0058] Hereinafter, various examples and embodiments of the present disclosure and its aspects are described using several variants and/or alternatives. It is generally to be noted that, according to certain needs and constraints, all of the described variants and/or alternatives may be provided alone or in any conceivable combination (also including combinations of individual features of the various variants and/or alternatives). In this description, the words comprising and including should be understood as not limiting the described examples and embodiments to consist of only those features that have been mentioned, and such examples and embodiments may also contain structures, units, modules, networks, etc. that have not been specifically mentioned.

[0059] In the drawings, it is to be noted that lines/arrows interconnecting individual blocks or entities are generally meant to illustrate an operational coupling there-between, which may be a physical and/or logical coupling, which on the one hand is implementation-independent and on the other hand may also comprise an arbitrary number of intermediary functional blocks or entities not shown.

[0060] According to embodiments of the present disclosure, in general terms, there is provided a highly linear multiplier, i.e. a multiplier capable of realizing a multiplication with high accuracy, especially a Gilbert-type multiplier in CMOS technology.

[0061] When hereinafter reference is made to a transconductance, this can mean a transconductance as an electrical characteristic relating a current through the output of a device, unit or element to a voltage across the input of the device unit or element (i.e. the reciprocal of resistance) or a transconductance element as a structural means (e.g. a device, unit or element) exhibiting a transconductance property (i.e. a transconductance-related transfer function). Also, a transconductance stage refers to a structural means including a transconductance, namely a transconductance property or element, such that a voltage across its input is converted into a current at its output.

[0062] FIG. 4 shows an example of a circuit diagram of a multiplier according to an embodiment. The multiplier shown in FIG. 4 is an analog multiplier which is based on transconductances or, stated in other terms, an analog multiplier based on the Gilbert principle (i.e. a Gilbert-type multiplier).

[0063] As shown in FIG. 4, the multiplier 1A is an analog multiplier which is configured to produce an output current i.sub.0 representing a product of a first input voltage vx and a second input voltage v.sub.y.

[0064] According to the Gilbert principle, the following can generally be said about the multiplier 1A. In a first unit, the first input voltage vx is converted with transconductance G11 into a current change i.sub.1, wherein transconductance G11 is operated with a constant bias current I.sub.bias1. To this current change, a constant bias current I.sub.bias2B (of transconductance G2B/G2B) is added and fed as bias current into transconductances G2B and G2B, wherein G2B receives the positively oriented portion of the current change i.sub.1 (i.e. the output current of a positive/+ output, corresponding to e.g. I(v.sub.muIP) in FIG. 2(a)) and G2B receives the negatively oriented portion of the current change i.sub.1 (i.e. the output current of a negative/ output, corresponding to e.g. I(v.sub.muIN) in FIG. 2(a)). The second input voltage v.sub.y is applied, in both polarities, to a second unit with a transconductance G2A/G2A, wherein transconductance G2A/G2A is operated with a constant bias current I.sub.bias2A, respectively. A voltage v.sub.d, which is a pre-distorted voltage of the second input voltage v.sub.y, is converted with transconductance G2B/G2B into a current change i.sub.2, wherein transconductance G2B/G2B is operated with bias current corresponding to the respective portion of the current change respectively. The output current changes i.sub.2 of transconductance G2B and G2B (each of which is a pair of differential currents, like i.sub.1) are combined with subtraction to form the resulting current i.sub.0, which is proportional to the product of the input voltages v.sub.x and v.sub.y.

[0065] As shown in FIG. 4, the multiplier 1A comprises a first transconductance stage 10 (with transconductance G11) which is configured to input the first input voltage v.sub.x and to output a first pair of differential currents i.sub.1, when being supplied with a first fixed bias current I.sub.bias1, wherein the first transconductance stage 10 comprises a negative feedback network (indicated by FB). Further, the multiplier 1A comprises a pair of second transconductance stages 20 (with transconductance G2A/G2A), each of which is configured to input the second input voltage v.sub.y and to output a pre-distorted voltage v.sub.d of the second input voltage v.sub.y, when being supplied with a second fixed bias current I.sub.bias2A, wherein each second transconductance stage 20 comprises a negative feedback network (indicated by FB). Further, the multiplier 1A comprises a pair of third transconductance stages 30 (with transconductance G2B/G2B), each of which is configured to input a voltage corresponding to the pre-distorted voltage v.sub.d of the second input voltage (in the example of FIG. 4, the pre-distorted voltage v.sub.d as such) and to output a second pair of differential currents i.sub.2, when being supplied with a bias current corresponding to a respective current of the first pair of differential currents i.sub.1. Further, the multiplier 1A comprises a combination network (40) which is configured to generate the output current i.sub.0 by combining the second pairs of differential currents i.sub.2 from both of the pair of third transconductance stages 30.

[0066] Any one of the aforementioned transconductances G11, G2A/G2A and G2B/G2B, i.e. the internal transconductance properties of the transconductance elements in the transconductance stages, basically corresponds to Gm in FIG. 2(b).

[0067] Although the exemplary circuit structure of FIG. 4 comprises a pair of second transconductance stages 20, it is to be noted that a single second transconductance stage is sufficient when a voltage corresponding to its output, i.e. the pre-distorted voltage v.sub.d, is applied to both transconductance stages 30, with corresponding signs/polarities, respectively.

[0068] In the exemplary circuit structure of FIG. 4, each transconductance stage can comprise a differential pair, such as a differential pair of CMOS transistors with the respective bias current as common/tail current. Accordingly, each one of transconductance stage 10, 20 and 30, i.e. the respective transconductance G11, G2A/G2A and G2B/G2B, can be realized in accordance with the circuit structure of FIG. 1.

[0069] As is evident from FIG. 4, the multiplier 1A comprises a linearized voltage-input unit for inputting the first input voltage v.sub.x, which corresponds to the first transconductance stage 10, and a linearized voltage-input unit for inputting the second input voltage v.sub.y, which corresponds to a combination of the at least one second transconductance stage 20 and a respective third transconductance stage 30. That is to say, the overall transfer function of the voltage-input units is linearized, although their internal transconductance properties (i.e. the transconductances G11, G2A/G2A and G2B/G2B) are highly non-linear, as is evident from FIG. 2(b).

[0070] In the following, the linearization of the voltage-input units, i.e. their overall transfer functions or transconductance properties, according to the present disclosure is explained.

[0071] FIG. 5 shows an example of a circuit diagram of a voltage-input unit which is applicable in a multiplier according to an embodiment. The voltage-input unit 15 shown in FIG. 5 represents a transconductance stage with a negative feedback network, and can be used as a first transconductance stage 10 in the multiplier of FIG. 4.

[0072] As shown in FIG. 5, the transconductance G11 is given a parallel output at the positive and negative output, which outputs the same current, i.e. +i.sub.1 or i.sub.1. Circuits with identical positive and negative current output have a similarity to current conveyors, and identical currents can be realized, for example, with current mirrors in CMOS technology. Each output current, i.e. +i.sub.1 or .sub.1, is compared with a reference current I.sub.bias1o by subtracting them from each other. The reference current I.sub.bias1o is identical in amount to the current i.sub.1 at the operating point, e.g. at an input differential voltage of 0.

[0073] When an input differential voltage v.sub.1 is applied, a voltage swing is generated at the output of the transconductance G11, where i.sub.1 and I.sub.bias1o are combined. This causes a current flow through feedback resistor/resistance R.sub.fb and causes a negative feedback together with the input resistor/resistance R.sub.in.

[0074] The output voltage of the transconductance G11 is not primarily relevant, since the current of the second identical output is evaluated. Nevertheless, the transconductance G11 can be regarded as an inverting voltage amplifier. In order to calculate the transconductance of the inverting circuit, the current difference generated by I.sub.bias1oi.sub.1 can be allowed to flow via the feedback resistor/resistance Rfb and the input resistor/resistance Rin to input v.sub.1. Since the direct input differential voltage at the transconductance G11, i.e. the voltage v.sub.d, is regulated to a small value by the negative feedback, the input resistor/resistance Rin determines the overall transconductance. Due to the negative feedback, the resulting overall transconductance hardly depends on the transconductance of the differential pair in the transconductance stage (which corresponds to G.sub.m in FIG. 2(b)). Accordingly, the non-linearity caused by the voltage control of the differential stage due to the very nonlinear G.sub.m can be dispelled or at least significantly mitigated by way of the negative feedback.

[0075] Therefore, the unit 15 and its overall transfer function or transconductance property, namely the current-voltage transfer function (i.e. the conversion from v.sub.1 or v.sub.x to i.sub.1), can be linearized with the exemplary circuit structure of FIG. 5.

[0076] FIG. 6 shows an example of a circuit diagram of another voltage-input unit which is applicable in a multiplier according to an embodiment. The voltage-input unit 25 shown in FIG. 6 represents a coupling of a transconductance stage with a negative feedback network and a subsequent transconductance stage (without a negative feedback network), and can be used as a combination of second and third transconductance stages 20 and 30 in the multiplier of FIG. 4.

[0077] As shown in FIG. 6, two transconductance stages are used in concatenation, which are featured in that their transconductances G2A and G2B have the same properties. Having the same properties can mean or comprise that a transconductance of a preceding transconductance stage is at least substantially equal to a transconductance of a subsequent transconductance stage which is configured to input the voltage based on the (pre-distorted) voltage from the preceding transconductance stage. Additionally or alternatively, having the same properties can mean or comprise that a preceding transconductance stage and a subsequent transconductance stage which is configured to input the voltage based on the (pre-distorted) voltage from the preceding transconductance stage are matched to each other. Such equivalence of properties can be achieved by arranging the two input portions/stages of G2A and G2B side by side in the physical layout, or even by arranging the transistors together in a so-called quad layout or inter-digitated layout.

[0078] Similar to the case of FIG. 5, an output current of the transconductance G2A, i.e. +i.sub.2A or i.sub.2A, is compared with a reference current I.sub.bias2o by subtracting them from each other. The reference current I.sub.bias2o is identical in amount to the current i.sub.2A at the operating point, e.g. at an input differential voltage of 0. When an input differential voltage v.sub.in2 is applied, a voltage swing is generated at the output of the transconductance G2A, where i.sub.2 and I.sub.bias2o are combined. This causes a current flow through feedback resistor/resistance R.sub.fb and causes a negative feedback together with the input resistor/resistance R.sub.in.

[0079] The transconductance G2A is operated/supplied with a fixed bias current I.sub.bias2A The bias current I.sub.bias2A is preferably chosen to be in the middle of the operating range of the bias current of the subsequent transconductance G2B, i.e. the variable signal input current i.sub.in2. Further, the bias current I.sub.bias2A can be chosen to minimize the non-linearity of the signal input i.sub.in2, which is already low when coming from a linearized transconductance stage like that shown in FIG. 5.

[0080] At the same time, the gain of the transconductance G2A is preferably selected to be significantly smaller than so that the feedback around the transconductance G2A at the direct input thereof causes the voltage v.sub.d to be set so that it generates the same current in the transconductance G2B as in the transconductance G2A, i.e. i.sub.2A=i.sub.2B. With a normal operational amplifier circuit, the gain, or more precisely the Gm of the input differential stage, would be set as high as possible, so that the voltage gain would ideally become 00 to minimize v.sub.d and thus obtain the highest possible linearity. Here, however, the gain should only be chosen high enough to minimize v.sub.d only so far to achieve sufficient linearity at the input level of the input differential voltage V.sub.in2. Referring to FIG. 6, it can be said that the transconductance G2A of the second transconductance stage and the transconductance G2B of the third transconductance stage should be chosen not too high, i.e. sufficiently low, so as to enable a mutual matching of/between the second and third transconductance stages. More specifically, the Gm of the input differential stage of the second and third transconductance stages should be chosen such that VgsVth of its transistors is not too small such that a mismatch of Vth between the transistors (of the two transconductance stages) does not (at least, not excessively or overly) affect the mutual matching of/between the second and third transconductance stages.

[0081] Thus, the transconductance G2B represents a transconductance stage linearized by a pre-distortion due to the negative feedback in the preceding transconductance G2A.

[0082] Hence, the transconductance G2A can be regarded as a multiplier (which can also be considered as an amplifier with adjustable gain) that multiplies v.sub.in2 by I.sub.bias2A, wherein I.sub.bias2A is constant and only v.sub.in2 is variable. By the negative feedback by way of the feedback resistor/resistance Rfb and the input resistor/resistance Rin, linearization is achieved and v.sub.d is (pre-) distorted accordingly. The multiplication of voltage and variable current is then realized by the transconductance G2B by processing the variable current i.sub.in2 with the pre-distorted voltage v.sub.d. Accordingly, the non-linearity caused by the voltage control of the differential stage due to the very nonlinear G.sub.m can be dispelled or at least significantly mitigated by way of the (pre-)distortion by the preceding differential stage and its negative feedback.

[0083] Accordingly, the unit 25 and its overall transfer function or transconductance property, namely the current-voltage transfer function (i.e. the conversion from v.sub.in2 or v.sub.y to i.sub.2B), can be linearized with the exemplary circuit structure of FIG. 6. That is, the transconductance stage of transconductance G2B, which is stacked on top of the transconductance stage of transconductance G11, can be linearized in that it is driven with a (pre-)distorted voltage which compensates for the non-linearity of the voltage drive.

[0084] FIG. 7 shows another example of a circuit diagram of a multiplier according to an embodiment. Similar to FIG. 4, the multiplier shown in FIG. 7 is an analog multiplier which is based on transconductances or, stated in other terms, an analog multiplier based on the Gilbert principle (i.e. a Gilbert-type multiplier), and is an analog multiplier which is configured to produce an output current i.sub.0 representing a product of a first input voltage v.sub.x and a second input voltage v.sub.y.

[0085] As shown in FIG. 7, the multiplier 1B has a basic configuration similar to that of the multiplier 1A of FIG. 4. Namely, the multiplier 1B comprises a first transconductance stage 10, a pair of second transconductance stages 20, a pair of third transconductance stages 30, and a combination network 40, which have the same/equivalent functionalities and structures as described above in connection with FIG. 4. Hence, a detailed description thereof is omitted.

[0086] More specifically, the multiplier 1B has a configuration in which a linearized voltage-input unit 15 as shown in FIG. 5 is adopted for the first transconductance stage 10, and a linearized voltage-input unit 25 as shown in FIG. 6 is adopted for both pairs of the second and third transconductance stages 20 and 30, respectively. Stated in other terms, the linearized transconductance of FIG. 5 for the first (lower) stage of stacked (or cascaded) transconductance is connected to the second (upper) stage of stacked (or cascaded) transconductance, which is driven by a variable current, like in the linearized transconductance unit of FIG. 6. Hence, for a detailed description, reference can be made to the description of FIGS. 5 and 6, in addition to the description of FIG. 4.

[0087] In brief, the functionality of the multiplier 1B can be outlined as follows. The multiplier 1B has two input voltages, namely v.sub.x and v.sub.y. The input voltage v.sub.x is converted by means of the linearized transconductance G11 into a current i.sub.x, which is fed, as second factor for product formation, with complementary sign into the transconductances G2B and G2B as bias current. For operating point adjustment, a current I.sub.bias2B is added to the variable current i.sub.x. The multiplier stages G2B and G2B are controlled by the pre-distortion stages G2A and G2A, which each provide a voltage v.sub.d at the transconductances G2B and G2B and ensure a linearized v.sub.y control of the multiplier stages. Since v.sub.d at the inputs of the transconductance stages G2B and G2B are identical, the transconductance stage G2A can be saved, and the voltage v.sub.d generated by the transconductance stage G2A can be fed not only to the transconductance stage G2B but also to the transconductance stage G2B.

[0088] FIG. 8 shows an example of a modulation characteristic (i.e. the signal changes) of the multiplier in line with the circuit diagram of FIG. 7 according to an embodiment.

[0089] The values on the y-axis are the currents of the positive and negative outputs of the transconductance stages G2B and G2B. The second input voltage v.sub.y is plotted on the x-axis, and the operating point is marked on the bisecting line of the angle when v.sub.x=0 and v.sub.y>0.

[0090] In the first quadrant are the current components for y+>0, and in the fourth quadrant are the current components for y<0. In case of v.sub.x>0, the operating lines of the transconductance stage G2B turn to larger absolute values (i.sub.x+y+, i.sub.x+y), and the operating lines of the transconductance stage G2B turn to smaller absolute values (i.sub.xy+, i.sub.xy). To calculate the product, the currents i.sub.x+y+ are connected to i.sub.x, and the currents i.sub.xy+ to i.sub.x+y, and then subtracted from each other, as shown in FIG. 7.

[0091] Accordingly, the combination network 40 can be configured to generate the output current (representing a product of a first input voltage and a second input voltage) by appropriately combining respective currents (or, differential currents). Namely, by appropriately connecting signal lines carrying respective currents, these currents are (implicitly) added/subtracted. When combining differential currents, a differential-to-unipolar conversion is also performed by the combination network 40 when a unipolar (singular) output current is intended to be generated as output. Accordingly, the combination network 40 generates the output current by subtracting a value, which is obtained by/as a combination of a positively oriented portion of an output current (i.e. the output current of a positive/+ output) of a third transconductance stage (which is operated/supplied with a negatively oriented portion of an output current (i.e. the output current of a negative/output) of the first transconductance stage) with a negatively oriented portion (i.e. the output current of a negative/output) of an output current of a third transconductance stage (which is operated/supplied with a positively oriented portion of an output current (i.e. the output current of a positive/+ output) of the first transconductance stage), from a value, which is obtained by/as a combination of a negatively oriented portion of an output current (i.e. the output current of a negative/output) of a third transconductance stage (which is operated/supplied with a negatively oriented portion of an output current (i.e. the output current of a negative/output) of the first transconductance stage) with a positively oriented portion (i.e. the output current of a positive/+ output) of an output current of a third transconductance stage (which is operated/supplied with a positively oriented portion of an output current (i.e. the output current of a positive/+ output) of the first transconductance stage).

[0092] FIG. 9 shows an example of an operating process or signal flow of the multiplier in line with the circuit diagram of FIG. 7 according to an embodiment. Namely, FIG. 9 shows an operating process or signal flow of a linearized multiplier according to an embodiment.

[0093] The schematic diagram shown in FIG. 9 illustrates the operation of the multiplier in line with the circuit diagram of FIG. 7, i.e. the operating process (i.e. method of operating the multiplier) or the signal flow thereof. As the thus shown operation is merely an illustration of what is described before in terms of the operability of the multiplier and its parts, the contents of FIG. 9 is held to be self-explanatory for the skilled person such that a detailed description thereof is omitted while making reference to the above description in connection with FIG. 7 (as well as FIGS. 4 to 6).

[0094] By way of example, referring to FIG. 7, the stage 10 converts the first input voltage to a current using the linearized transconductance, and any one of stages 20 converts the second input voltage to a (pre-)distorted voltage using the linearized transconductance. The current from the stage is subtracted from a bias current of a first transconductance of the upper stage 30, and the upper stage 30 uses the (pre-)distorted voltage from the upper stage 20 as input voltage. The current from the stage 10 is added to a bias current of a second transconductance of the lower stage 30, and the lower stage 30 uses the (pre-)distorted voltage from the lower stage 20 as input voltage. Then, the combination network 40 combines the outputs from the first and second transconductances, i.e. the upper and lower stages 30.

[0095] FIG. 10 shows examples of transistor circuits of various parts of/for a multiplier according to an embodiment. That is, any one of the transistor circuits shown in FIG. 10 can be implemented/realized alone or in a multiplier such as any one of the multipliers 1A, 1B and 1C exemplified herein.

[0096] As shown in FIG. 10, the parts of a multiplier can be realized with CMOS transistors. In FIG. 10, the same reference numerals as in FIG. 7 are used for denoting parts serving as corresponding stages or units of a multiplier, respectively. The relationship/connection between the individual parts, when being integrated into a multiplier as shown in FIG. 7, becomes evident from the mutually corresponding denominations of their signals. For example, the currents I(V.sub.MP) and I(V.sub.MN) in part 10 serving as a first transconductance stage are fed as currents to part 30 serving as a third transconductance stage, and the voltages V.sub.YinPG2 and V.sub.YinNG2 in part 20 serving as a second transconductance stage are input as voltages to part 30 serving as a third transconductance stage, respectively.

[0097] In order for the multiplier (resulting from a combination of the parts shown in FIG. 10) to work with low supply voltages, the first transconductance stage 10, i.e. the differential pair of transconductance G11, is built with NMOS transistors, namely with a NMOS input stage/portion, and the second and third transconductance stages 20 and 30, i.e. the differential pair of transconductances G2A, G2A, G2B and G2B, are built with PMOS transistors, namely with a PMOS input stage/portion, respectively. Any current mirrors and loads are not realized on transistor level here but with dummy voltage sources with a voltage of 0 V. These dummy voltage sources with the designations V.sub.M . . . are used to measure the respective current that controls the current-controlled current sources I(V.sub.M . . . ). For example, V.sub.MP and V.sub.MN measure the current of the first transconductance G11, and these currents are reproduced with I(V.sub.MN) in transconductance G2B and I(V.sub.MP) in transconductance G2B. On transistor level, this function can be realized with current mirrors.

[0098] In the first transconductance stage 10, the first transconductance G11 processes the first input voltage v.sub.x, which is applied as V.sub.XinP and V.sub.XinN to the input of and G11. Firstly, the generated currents of the first transconductance G11 are used to control the tail current of the transconductances G2B and G2B, i.e. as output current. Secondly, for realizing a negative feedback, the generated currents of the first transconductance G11 are compared with bias current source I.sub.biasI.sub.gain/2. The factor I.sub.gain is used to adjust the gain and hence the level of negative feedback of the first transconductance G11, and thus controls the level of linearization of the first transconductance G11.

[0099] In the second and third transconductance stages 20 and 30, the gate nodes V.sub.YinNG and V.sub.YinPG of the transconductances G2A and G2B are connected to each other via the labels on the wires. The same applies to the gate nodes V.sub.YinNG2 and V.sub.YinPG2 for the transconductances G2A and G2B. The transconductances G2A and G2A generate voltages through the negative feedback network at the input nodes of the differential stage, which cause differential currents in the matched transconductances G2B and G2B that are proportional to the second input voltage v.sub.y. Since the operating current of the transconductances G2B and G2B, which is controlled by the first transconductance stage 10, is proportional to the first input voltage v.sub.x, a multiplication of the input voltages v.sub.x and v.sub.y is effectively performed in the transconductances G2B and G2B. Then, in the combination network 40, the results of the differential currents of the transconductances G2B and G2B are combined by means of current-controlled voltage sources CCVS1 to CCVS4 with the correct sign to obtain the multiplication result VOUT.

[0100] FIG. 11 shows an example of a modulation characteristic of the multiplier in line with the transistor circuits of FIG. 10 according to an embodiment, namely a result of a transistor simulation.

[0101] As shown in FIG. 11, the second input voltage v.sub.y is varied on the x-axis, and the first input voltage v.sub.x is changed as a parameter in steps of 100 mV. The straight lines and the equidistant y-sections at v.sub.y=400 mV, show the accuracy of the multiplier in the realization as shown in FIG. 10.

[0102] Due to the multiplication of small numerical values, i.e. the multiplication of currents in the A range, small numerical values in the nV range are produced in the model of the multiplier with the current-controlled voltage sources of the multiplier in the realization as shown in FIG. 10, which, however, produce considerably larger voltage levels in a real transistor circuit.

[0103] FIG. 12 shows an example of a linearity characteristic of the multiplier in line with the transistor circuits of FIG. 10 according to an embodiment, namely a result of a transistor simulation.

[0104] As shown in FIG. 12, the linearity of multiplier in the realization as shown in FIG. 10 can be recognized from the plotted derivation of the characteristic curves. The derivatives are exactly equidistant at 0.5, and even at a level of v.sub.y=270 mV and v.sub.x=400 mV (i.e. the upper marker), the deviation of the derivative from the nominal value of 2.00 is less than 0.5% at 1.991. At a level of v.sub.y=300 mV and v.sub.x=100 mV (i.e. the lower marker), the derivate does not even show any deviation but lies at the nominal value of 500 n such that no error is present at this point.

[0105] As explained above, a multiplier with improved linearity, especially a Gilbert-type multiplier in CMOS technology, can be realized with the circuit structures of FIG. 4, 7 or 9. However, the linearity can still be further enhanced, as is explained below.

[0106] When linearizing the transconductances G2B and G2B by the transconductances G2A and G2A, i.e. providing the voltage-input unit 25, as shown in FIGS. 6 and 7, it is assumed that the voltage v.sub.d formed by the transconductance G2A/G2A corresponds exactly to the inverse function of the transconductance G2B/G2B, which converts the voltage v.sub.d at its input into the currents i.sub.xy+ and i.sub.xy+. Yet, this assumption would only be valid if the transconductance property G.sub.m in the transconductance element G2B is exactly proportional to the bias current I.sub.bias2Bi.sub.x, and the transconductance property G.sub.m in the transconductance element G2B is exactly proportional to the bias current I.sub.bias2B+i.sub.x. Due to the finite amplification of the transconductance G2A/G2A, there are however further possible deviations from the desired inverse function.

[0107] FIG. 13 shows examples of error characteristics with respect to a first input voltage of the multiplier in line with the circuit diagram of FIG. 7 according to an embodiment, and FIG. 14 shows examples of error characteristics with respect to a second input voltage of the multiplier in line with the circuit diagram of FIG. 7 according to an embodiment. That is, FIGS. 13 and 14 represent results of simulations based on the circuit diagram of FIG. 7 (with an implementation of the individual parts/units in line with the transistor circuits as illustrated in FIG. 10).

[0108] As shown in FIG. 13, the first input voltage v.sub.x is traversed from 1 V to +1 V, the second input voltage v.sub.y is the parameter that is increased from 0 V to 1 V with a step size of 0.1 V. The individual graphs in FIG. 13 are from top to bottom: a multiplication result in FIG. 13(a), an absolute error in FIG. 13(b) and a relative error in FIG. 13(c).

[0109] As shown in FIG. 14, the second input voltage v.sub.y is traversed from 1 V to +1 V, the second input voltage v.sub.x is the parameter that is increased from 0 V to 1 V with a step size of 0.1 V. The individual graphs in FIG. 14 are from top to bottom: a multiplication result in FIG. 14(a), an absolute error in FIG. 14(b) and a relative error in FIG. 14(c).

[0110] As a basis for the error calculation, multiplication coefficients calculated at v.sub.x=0.1 V and v.sub.y=0.1 V are used. From FIG. 13(c), the following can be recognized: For large v.sub.y, the error hardly depends on v.sub.x and is up to 1%, corresponding to 1010.sup.3=10 mV. In case of v.sub.y=100 mV, the relative error ranges between 0 at v.sub.x=100 mV, because the error calculation is normalized to 100 mV, and a maximum of about 0.1%. The relative error curves in FIG. 13(c) are not equidistant. This fact is reflected in the approximate parabolic shape of the relative error, if v.sub.y is varied continuously and v.sub.x is used as the parameter that is changed stepwise from 0 V to 1 V. Such an error curve is shown in FIG. 14(c).

[0111] In view of such findings, the linearization of the transconductances G2B and G2B by the transconductances G2A and G2A, can be further improved.

[0112] According to an embodiment, a multiplier comprises an error compensating circuit which is configured to generate a compensated voltage for compensating an error in the output current with respect to an exact algebraic product of the first input voltage and the second input voltage.

[0113] FIG. 15 shows still another example of a circuit diagram of a multiplier according to an embodiment. Similar to FIGS. 4 and 7, the multiplier shown in FIG. 15 is an analog multiplier which is based on transconductances or, stated in other terms, an analog multiplier based on the Gilbert principle (i.e. a Gilbert-type multiplier), and is an analog multiplier which is configured to produce an output current i.sub.0 representing a product of a first input voltage v, and a second input voltage v.sub.y.

[0114] As shown in FIG. 15, the multiplier 1C has a basic configuration similar to that of the multiplier 1B of FIG. 7. Namely, the multiplier 1C comprises a first transconductance stage 10, a second transconductance stage 20, a pair of third transconductance stages 30, and a combination network 40, which have the same/equivalent functionalities and structures as described above in connection with FIGS. 4 and 7. Hence, a detailed description thereof is omitted. It is to be noted that in the circuit structure of FIG. 15, a single second transconductance stage 20 is used for providing a pre-distorted voltage of the second input voltage, and a voltage based on this pre-distorted voltage (i.e. a compensated voltage v.sub.Ycomp) is input to both of the pair of third transconductance stages 30, respectively.

[0115] As compared with the circuit structure of FIG. 7, the multiplier 1C of FIG. 15 is however extended by a compensation circuit, which is configured to reduce the error (which error reduction can, by way of simulations, be by a factor of about 10, as is shown below in FIGS. 16 and 17). According to an embodiment, the compensation circuit is realized by a combination of a second transconductance stage 20, a fourth transconductance stage 50 and a multiplication-addition network 60, which in the circuit structure of FIG. 15 replaces a second transconductance stage 20 in the circuit structure of FIG. 7.

[0116] As shown in FIG. 15, the compensation circuit in the multiplier 1C generates a compensated voltage v.sub.Ycomp. Namely, the transconductance stage 20 generates a pre-distorted voltage v.sub.dGA2, as explained above, and the transconductance stage 50 generates a scaled voltage v.sub.G3 (by applying a gain, without providing a negative feedback). Then, the pre-distorted voltage v.sub.dGA2 is multiplied with a factor ky, the scaled voltage v.sub.G3 is multiplied with a factor (1ky), and the resulting multiplied voltages are added (by an adder/summator) to produce the compensated voltage v.sub.Ycomp, i.e. v.sub.Ycomp=v.sub.dGA2ky+v.sub.G3(1ky). The thus produced compensated voltage v.sub.Ycomp is input to the third transconductance stages 30, i.e. the transconductance G2B and G2B, respectively.

[0117] It is to be noted that multiplication with ky and (1ky) can be realized by a multiplier but does not require a multiplier. Rather, such multiplication can be realized with voltage dividers or potentiometers, since the multiplication is done with a constant.

[0118] If ky=1, the output voltage of the transconductance G3 (v.sub.G3) has no effect, since v.sub.G3 is multiplied by 0, while the output voltage of the transconductance G2A (v.sub.dGA2) is used as compensated voltage, since v.sub.dGA2 is multiplied by 1. The circuit structure of FIG. 15 then has the same function as the circuit structure of FIG. 7.

[0119] As explained above, the factor ky for error compensation can be chosen between 0 and 1. If so, the voltages v.sub.dGA2 and v.sub.G3 are multiplied by ky and (1ky), and the sum of the factors ky and (1ky) is equal to 1. In the illustrated example, which generates the simulation results of FIGS. 13 and 14, ky can preferably be set to 0.45 to achieve optimal error compensation (i.e. error compensation by a factor 10).

[0120] However, the factor ky for error compensation can be chosen to be greater than 1, e.g. 10. If so, the voltages v.sub.dGA2 and v.sub.G3 are multiplied by ky and 1/ky, and the product of the factors ky and 1/ky is equal to 1, wherein a normalization by the factor ky can preferably be applied subsequently, i.e. before of after the adder/summator.

[0121] The factor ky for error compensation can be manually or automatically chosen. For example, the factor ky can be set by a user, operator, designer, etc. in view of simulation and/or test results, or the factor ky can be set by a control circuit (not shown) on the basis of simulations and/or tests, e.g. by way of a feedback control depending on a resulting simulated/tested error value, so as to minimize the error value.

[0122] Without additional error compensation, the voltage V.sub.dG2A generated by the second transconductance stage 20 would be fed directly to the voltage inputs of the transconductances G2B and G2B.

[0123] A transconductance G2A, i.e. an additional second transconductances stage, as shown in FIG. 7, is not necessary since the transconductances G2A and G2A generate the same voltage and, thus, the transconductances G2A is redundant, as indicated above. Anyway, the multiplier 1C can comprise two compensation circuits (each being equivalent to the compensation circuit shown in FIG. 15), wherein the compensated voltage of the one compensation circuit (corresponding to the transconductance G2A) is fed to the voltage input of the transconductance G2B, and the compensated voltage of the other compensation circuit (corresponding to the transconductance G2A) is fed to the voltage input of the transconductance G2B.

[0124] According to the embodiment of FIG. 15, the multiplier 1C comprises at least one fourth transconductance stage 50 (with transconductance G3) which is configured to input the second input voltage and to output a scaled voltage of the second input voltage, when being supplied with a third fixed bias current, and at least one multiplication-addition network 60 which is configured to generate a compensated voltage of the second input voltage by multiplying the pre-distorted voltage of the second input voltage from a second transconductance stage by a first factor, multiplying the scaled voltage of the second input voltage from a fourth transconductance stage by a second factor and adding the multiplied pre-distorted voltage and the multiplied scaled voltage, wherein each third transconductance stage 30 is configured to input the compensated voltage of the second input voltage from a multiplication-addition network 60.

[0125] FIG. 16 shows examples of error characteristics with respect to a first input voltage of the multiplier in line with the circuit diagram of FIG. 15 according to an embodiment, and FIG. 17 shows examples of error characteristics with respect to a second input voltage of the multiplier in line with the circuit diagram of FIG. 15 according to an embodiment. That is, FIGS. 16 and 17 represent results of simulations based on the circuit diagram of FIG. 15 (with an implementation of the individual parts/units in line with the transistor circuits as illustrated in FIG. 10).

[0126] As the graphs of FIGS. 16 and 17 are equivalent to the graphs of FIGS. 13 and 14, reference is made to their description for details, while a repeated description is omitted here. As indicated above, the graphs of FIGS. 16 and 17 result from a simulation on the basis of the circuit diagram of FIG. 15 when a factor ky of 0.45 is applied.

[0127] By way of a comparison of FIGS. 16 and 17 with FIGS. 13 and 14, it can be recognized that an error compensation by a factor of 10 can be achieved. Namely, if the multiplier is linearized at v.sub.x0=0.1 V and v.sub.y0=0.1 V, all relative errors are less than 0.1%.

[0128] FIG. 18 shows an example of an operating process or signal flow of the multiplier in line with the circuit diagram of FIG. 15 according to an embodiment. Namely, FIG. 18 shows an operating process or signal flow of a linearized and error-compensated multiplier according to an embodiment.

[0129] The schematic diagram shown in FIG. 18 illustrates the operation of the multiplier in line with the circuit diagram of FIG. 15, i.e. the operating process (i.e. method of operating the multiplier) or the signal flow thereof. As the thus shown operation is merely an illustration of what is described before in terms of the operability of the multiplier and its parts, the contents of FIG. 15 is held to be self-explanatory for the skilled person such that a detailed description thereof is omitted while making reference to the above description in connection with FIG. 15 (as well as FIGS. 4 to 7).

[0130] By way of example, referring to FIG. 15, the stage 10 converts the first input voltage to a current using the linearized transconductance, the stage 20 converts the second input voltage to a (pre-)distorted voltage using the linearized transconductance, and the stage 50 converts the second input voltage to a voltage using a gain (transconductance). The stage 60 combines the outputs from the stages 20 and 50 to generated a compensated voltage. The current from the stage 10 is subtracted from a bias current of a first transconductance of the upper stage 30, and the upper stage 30 uses the compensated voltage from the stage 60 as input voltage. The current from the stage 10 is added to a bias current of a second transconductance of the lower stage 30, and the lower stage 30 uses the compensated voltage from the stage 60 as input voltage. Then, the combination network 40 combines the outputs from the first and second transconductances, i.e. the upper and lower stages 30.

[0131] As explained above, a multiplier with even further improved linearity, especially a Gilbert-type multiplier in CMOS technology, can be realized with the circuit structures of FIG. 15.

[0132] In the foregoing, various examples and embodiments for realizing a highly linear multiplier, i.e. a multiplier capable of realizing a multiplication with high accuracy, especially a Gilbert-type multiplier in CMOS technology, are disclosed.

[0133] The thus disclosed examples and embodiments are for illustrative purposes, without limiting the present disclosure. For example, analog multipliers are exemplified, i.e. configurations in which analog input signals (e.g. voltages) are multiplied to produce an analog output signal (e.g. current). The present disclosure is, however, not limited to such (completely) analog configuration, and equally encompasses fully or partly digital configurations, such as e.g. a combined analog-digital (design of a) multiplier. In such analog-digital (design of a) multiplier, an analog signal could be subjected to pulse width modulation (PWM) and the PWM signal could be used as an input signal, and/or the reference signal of a digital-to-analog converter (DAC) could be used as the one analog input signal and the digital input of the DAC could be used as the other analog input signal, for example.

[0134] While in the foregoing reference is made to a multiplier, the thus disclosed circuit structures and configurations are generally applicable in/to any kind of electric circuit, unit or device. For example, the exemplified multipliers are applicable in/to a digital-to-analog converter (DAC) or any other element which could, at least under certain conditions and/or assumptions, be considered as (part of) a multiplier. Further, the exemplified multipliers are applicable in/to any kind of analog computing circuit or device as well as computers for (implementing/realizing) artificial intelligence, computers for (performing) neural signal processing, circuits or devices for (implementing/realizing) any kind of neural network, or the like. Accordingly, the present disclosure enables to build analog computing circuits or devices or analog computers based on CMOS technology, which are suitable and competitive in the field of artificial intelligence as well as neural signal processing and neural networking.

[0135] Moreover, it is noted that all of the exemplified parts, stages, units, etc. can be implemented and used alone or in any conceivable combination, with the illustrated circuit structures and configurations merely representing non-limiting examples. For example, the units of FIGS. 5 and 6 can be applied/used as such or in any kind of electric circuit, unit or device (even other than a multiplier), respectively.

[0136] As a further supplement/addition, the following explanations are applicable for and thus constitute part of the present disclosure.

[0137] A highly linear multiplier is provided, which exhibits at least part of the following features or attributes. [0138] Series-connected transconductance stages (differential stages) can be used. [0139] The transconductance stages (differential stages) at the input of input voltages are linearized by negative feedback. [0140] The transconductance stages (differential stages) can be realized with MOS or CMOS transistors as transconductances. [0141] A first signal input is converted by means of a linearized transconductance stage or transconductance into a current which is fed as working current into the transconductance stage (differential stage) of a second transconductance. [0142] The second transconductance is connected to a second signal input, and is linearized by using a third transconductance with negative feedback to convert the second signal input into a differential signal for the second transconductance which itself does not require negative feedback. [0143] The second transconductance can be implemented twice, one of the doubly implemented transconductances being fed with the positively oriented current from the first transconductance, the other of the doubly implemented transconductance being fed with the negatively oriented current from the first transconductance, and the currents from the two doubled transconductances are combined with the correct sign in order to generate an output signal which corresponds to that of a four-quadrant multiplier.

[0144] A highly linear multiplier is based on the following considerations. [0145] The non-linearity of a differential MOS or CMOS stage is essentially caused by the non-linear current-voltage conversion, and less by a non-proportional sharing of the common current in the differential stage when the input voltage is constant. [0146] The transconductance stages (differential stages), which are fed with the current from the first transconductance, are driven with a voltage which is pre-distorted with respect to the original second input voltage, so that the change of the differential current becomes proportional to the original second input voltage. [0147] The pre-distortion is performed by adding an equivalent or even (substantially) identical transconductance to the transconductance to be linearized, which has a negative feedback, so that the signal for driving the transconductance to be linearized is generated at the transistor input of this negative feedback transconductance.

[0148] A cascading of the transconductances can be realized, which is effective to achieve the function of a four-quadrant multiplier. In this regard, the first transconductance has at least two identical current outputs, where one current output is used for the negative feedback, and the other current output is used to provide the operating current for the subsequent or cascaded transconductance/s.

[0149] The error of the multiplier can be further reduced by applying the second signal input not only to a linearized transconductance (with a negative feedback) for pre-distortion, but also using the second signal input without pre-distortion, just scaled with a gain, which can e.g. be less than one.

[0150] Then, the scaled second input signal and a scaled portion of the pre-distorted second input signal are added, and the two transconductances, which process the pre-distorted second input signal as voltage and the first input signal as current, are fed to the voltage input.

[0151] The present disclosure also covers any conceivable combination of structural or functional elements described above, as long as the above-described concepts of methodology and structural arrangement are applicable.

[0152] In view of the above, there is provided a linearized multiplier configured to produce an output current representing a product of a first input voltage and a second input voltage, comprising: a first transconductance stage which is configured to input the first input voltage and to output a first pair of differential currents, wherein the first transconductance stage comprises a negative feedback network, at least one second transconductance stage which is configured to input the second input voltage and to output a pre-distorted voltage of the second input voltage, wherein each second transconductance stage comprises a negative feedback network, a pair of third transconductance stages, each of which is configured to input a voltage corresponding to the pre-distorted voltage of the second input voltage and to output a second pair of differential currents, when being supplied with a bias current corresponding to a respective current of the first pair of differential currents.

[0153] Even though the present disclosure is described above with reference to the examples according to the accompanying drawings, it is to be understood that the present disclosure is not restricted thereto. Rather, it is apparent to those skilled in the art that the present disclosure can be modified in many ways without departing from the scope of the inventive idea as disclosed herein.