# ENHANCED TRANSCONDUCTANCE CIRCUIT

- ANALOG DEVICES, INC.

A transconductance circuit that improves linearity and output current over a wider range of input voltages than prior designs. The transconductance circuit may include first and second sets of paired differential transistors. In each set, emitters of the paired transistors may be commonly coupled to corresponding nodes of a common impedance, and collectors may be coupled to output terminals of the transconductance circuit. The circuit may further include first and second sets of doublet differential transistor pairs, each doublet pair having transistors of different sizes. Each doublet pair may have current sources coupled between commonly coupled emitters and a source potential. Respective collectors for each doublet pair may be coupled to the output terminals of the transconductance circuit. A pair of voltage followers may be provided to replicate corresponding input voltages across corresponding bases of the differential transistor pairs and the doublet transistor pairs.

## Description

#### RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No. 13/424,961, filed on Mar. 20, 2012, the entirety of which is incorporated by reference herein.

#### BACKGROUND

Transconductance is a property of certain electronic circuits which relates to a ratio of a change in the output current generated by a circuit versus the change in input voltage supplied to the circuit. Transconductance may be referred to herein as “GM,” and can be represented mathematically as:

$G M = Δ   I OUT Δ   V IN Eqn .  1$

A transconductance circuit may be referred to as a “GM circuit.” Ideally, the transconductance of a GM circuit should remain linear with corresponding input voltage changes. Further, the output current of a GM circuit should track corresponding input voltage changes.

In application, however, linear transconductance and output current tracking is difficult to achieve. A GM circuit is often implemented using a differential pair of transistors as shown in the differential pair transconductance circuit 100 of FIG. 1, but this type of circuit suffers from known disadvantages.

The differential pair circuit 100 includes a pair of transistors Q1, Q2 having common emitter couplings. A current source ISOURCE is coupled to the common emitters of Q1, Q2 to bias the circuit. Output currents IOUTP, IOUTM are obtained from collectors of Q1 and Q2. A differential input signal VIN, is represented by the difference of voltages VINP, VINM, which are applied to the corresponding bases of Q1 and Q2. The circuit 100 generates a differential output current IOUT represented by the difference of output currents IOUTP, IOUTM.

As the input voltages VINP, VINM vary, the differential pair generates corresponding output currents IOUTP, IOUTM, which relate to the input voltages. FIG. 2 is a graph 200 illustrating a simulated transconductance and differential output current IOUT for the differential pair circuit 100 of FIG. 1. The simulated transconductance and differential output current IOUT are normalized for illustrative purposes.

As shown in FIG. 2, as a differential input voltage VIN is applied across the bases of Q1 and Q2 from −160 mV to 160 mV, transconductance (GM) of the circuit 100 is linear only for a small range of differential input voltages near 0V. As the differential input voltage VIN, varies away from 0V, the transconductance varies in a non-linear manner.

Further, the output current IOUT does not track changes of the differential input voltage VIN. Rather, IOUT only tracks changes in the differential input voltage VIN from approximately −20 mV to 20 mV, and then begins to saturate. The output current for the differential pair circuit 100 is limited by the output current from the current source ISOURCE.

The differential pair circuit 100 generates an undesirable output error for input voltages VINP, VINM that are supplied at common mode voltage levels. The error is a consequence of the finite output impedance for the current source ISOURCE. The output error exhibits rectification which also degrades the transconductance linearity for the differential pair circuit 100.

FIG. 3 illustrates a doublet transconductance circuit 300 (referred to as a “doublet circuit” herein). The doublet circuit 300 includes complementary sets of area-offset differential transistor pairs. A first set includes transistors, QU1.1, QU1.2 having a current source IU.1 coupled between emitters of each transistor and a first source potential VSS. A complementary transistor pair QL1.1, QL1.2 have a current source IU.2 coupled between emitters of each transistor and a second source potential VDD. A second set includes transistors QU2.1, QU2.2 having a current source IU.2 coupled between emitters of each transistor and the first source potential VSS. A complementary transistor pair QL2.1, QL2.2 have a current source IL.2 coupled between emitters of each transistor and the second source potential VDD.

A first input voltage VINP is applied to the bases of transistors QU1.1, QU2.1, QL1.1, and QL2.1. A second input voltage VINM is applied to the bases of transistors QU1.2, QU2.2, QL1.2, and QL2.2. Output currents IOUTP.1 and IOUTM.1 are obtained from the collectors of QU1.1-QU2.2 and represent half of an overall output current IOUT1 for the doublet circuit 300. Output currents IOUTP.2 and IOUTM.2 are obtained from the collectors of QL1.1-QL2.2 and represent half of an overall output current IOUT2 for the doublet circuit 300.

The transistors QU1.1-QU2.2 and QL1.1-QL2.2 have area offsets as represented by AOFF:1 where AOFF corresponds to an offset area factor among the transistors. Transistors QU1.2, QU2.1, QL1.2, and QL2.1 are larger than the other transistors by the offset factor AOFF. When activated, the area offset transistors conduct a correspondingly higher current than the smaller transistors.

FIG. 4 is a graph 400 simulating transconductance for the doublet circuit of FIG. 3 for various area offset factors. As illustrated in FIG. 4, the transconductance for the doublet circuit is flattened or “spread” for various area offset factors including AOFF=4 and AOFF=6. For an area offset factor of AOFF=1, the transconductance is similar to that of the differential pair circuit 100 of FIG. 1. As the area offset is increased to AOFF=4, the transconductance linearity is improved for differential input voltages VIN from approximately −20 mV to 20 mV. As the area offset is increased to AOFF=6, transconductance continues to spread but linearity is degraded.

Although the doublet circuit 300 provides improvements for transconductance linearity, the output current is limited similar to that of the differential pair circuit 100. The output current of the doublet circuit 300 is limited by the currents from the current sources IU.1, IU.2, IL.1, and IL.2.

Accordingly, there is a need in the art for a transconductance circuit that improves transconductance linearity and output current.

#### BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a differential pair transconductance circuit.

FIG. 2 is a graph simulating transconductance and differential output current for the differential pair circuit of FIG. 1.

FIG. 3 illustrates a doublet transconductance circuit.

FIG. 4 is a graph simulating transconductance for the doublet circuit of FIG. 3 for various area offset factors.

FIG. 5 illustrates a transconductance circuit according to an embodiment of the present invention.

FIG. 6 is a graph simulating transconductance and differential output current for the transconductance circuit of FIG. 5 versus that of the differential pair circuit of FIG. 1.

FIG. 7 illustrates an enhanced transconductance circuit according to an embodiment of the present invention.

FIG. 8 is a graph simulating transconductance and differential output current for the enhanced transconductance circuit of FIG. 7 versus that of the differential pair circuit of FIG. 1.

FIG. 9 is a method for generating a pair of output currents from a transconductance circuit which track voltage changes for a first predetermined range of input voltages according to an embodiment of the present invention.

FIG. 10 is a diagram of a differential amplifier for use with embodiments of the present invention.

#### DETAILED DESCRIPTION

Embodiments of the present invention provide a transconductance circuit that improves transconductance linearity and output current over a wider range of input voltages than prior designs. The transconductance circuit may include first and second sets of paired differential transistors, where, in each set, emitters of the paired transistors may be commonly coupled to corresponding nodes of a common impedance, and collectors may be coupled to output terminals of the transconductance circuit. The circuit may further include first and second sets of doublet differential transistor pairs, each doublet pair having transistors of different sizes. Each doublet transistor pair may have current sources coupled between commonly coupled emitters and a source potential. Respective collectors for each doublet transistor pair may be coupled to the output terminals of the transconductance circuit. A pair of voltage followers may be provided to replicate corresponding input voltages across corresponding bases of the complementary set of differential transistor pairs and the complementary sets of doublet transistor pairs.

As noted, the transconductance of a single differential pair is non-linear over a wide range of input voltages and the doublet circuit, while providing improvements for transconductance linearity, has limited output current. In the configuration of the embodiments described herein, non-linear behavior is mitigated in large part because non-linearities in the sets of differential transistor pairs are counter-acted by non-linearities in the sets of doublet transistor pairs. This phenomenon is discussed in greater detail herein below. Output current is also improved in the configuration of the embodiments described herein.

FIG. 5 illustrates a transconductance circuit 500 according to an embodiment of the present invention (referred to as an “I-bridge circuit” herein). The I-bridge circuit 500 may include complementary sets of differential transistor pairs. A first differential pair may include a first pair of transistors QU1.1, QU1.2, having emitters commonly coupled to a first node N1, and collectors coupled to corresponding output terminals IOUTP.1, IOUTM.1. A second differential pair may include a second pair of transistors QL1.1, QL1.2, having emitters commonly coupled to a second node N2, and collectors coupled to corresponding output terminals IOUTM.2, IOUTP.2. A common impedance R1 may be coupled between the first and second node N1, N2.

A pair of voltage followers FOLR.1, FOLR.2 may be coupled to bases of corresponding transistors QU1.1, QL1.1 and QU1.2, QL1.2. The voltage followers FOLR.1, FOLR.2 may replicate input voltages VINP, VINM at bases of the corresponding transistors. A first follower FOLR.1 may include a complementary pair of transistors QC1.1, QC1.2. Current sources IUB.1, ILB.1 may be coupled respectively to transistors QU1.1 and QL1.1. The first follower FOLR.1 may receive a first input voltage VINP and replicate corresponding voltages at bases of the transistors QU1.1, and QL1.1. A second follower FOLR.2 may include a complementary pair of transistors QC2.1, QC2.2. Current sources IUB.2, ILB.2 may be coupled to respective bases for transistors QU1.2, QL1.2. The second voltage follower FOLR.2 may receive a second input voltage VINM and replicate corresponding voltages at bases of the transistors QU1.2 and QL1.2.

Currents generated at outputs IOUTP.1 and IOUTM.1 each may represent one-half of an overall output current IOUT1 for the I-bridge circuit 500. Similarly, currents generated at outputs IOUTP.2 and IOUTM.2 each may represent one-half of an overall output current IOUT2 for the I-bridge circuit 500.

During operation, each follower FOLR.1, FOLR.2 may replicate corresponding voltages for driving the bases of each set of paired transistors from input voltage VINP, VINM. As the input voltages VINP, VINM may vary, each of the first pair of transistors QU1.1, QU1.2 may generate corresponding output currents IOUTP.1, IOUTM.1, which may relate to input voltage variations. Similarly, each of the second pair of transistors QL1.1, QL1.2 may generate corresponding output currents IOUTP.2, and IOUTM.2 which may relate to the input voltage variations.

The I-bridge circuit 500 improves transconductance linearity and output current over the differential pair of FIG. 1. FIG. 6 is a graph 600 simulating a transconductance and differential output current response IOUT for the I-bridge circuit 500 of FIG. 5 versus that of the differential pair of FIG. 1. FIG. 6(a) compares the transconductance linearity for both circuits for a range of differential input voltages VIN from −200 mV to 200 mV. FIG. 6(b) compares the differential output current response IOUT for both circuits across the voltage range. The output of each circuit type is normalized for comparative purposes.

As illustrated, transconductance linearity of the I-bridge circuit 500 is improved over that of the differential pair circuit 100 of FIG. 1. Coupling the resistor R1 between the first and second pairs of transistors may flatten the overall transconductance for the I-bridge circuit 500 (solid line). In contrast, the overall transconductance for differential pair circuit 100 (dashed line) varies greatly over the range of input voltages VIN.

The output current IOUT of the I-bridge circuit 500 is improved over that of the differential pair circuit. As illustrated, the output current of the I-bridge circuit 500 may track changes for differential input voltages VIN from approximately −200 mV to 200 mV without saturation. The output current of the I-bridge circuit 500 should not saturate because the first and second transistor pairs are not limited by the output current of a current source. In contrast, the output current of the differential pair circuit 100 is limited by the output current of current source ISOURCE and therefore begins to saturate as the differential input voltages VIN begin to diverge from 0 mV. In various embodiments, the output current for the I-bridge circuit 500 may be configured to track predetermined ranges of differential input voltages VIN by changing the value of the common impedance R1.

The I-bridge circuit 500 may also reduce output error current over the differential pair circuit of FIG. 1 for common mode input voltages. The complementary configuration of the first and second transistor pairs QU1.1, QU1.2, QL1.1, and QL1.2 and complementary current sources IUB.1, IUB.2, and ILB.1, ILB.2 may minimize the output error current. Although each transistor of the first and second transistor pairs individually may develop output error currents for common mode input voltages, the complementary configuration of each pair in the I-bridge circuit 500 may cause the respective error currents from each pair to effectively cancel each other out. Thus, the overall output error current of the I-bridge circuit 500 may be minimized for common mode voltages.

Noise levels for the I-bridge circuit 500 may also be minimized even with the addition of the impedance R1 coupled between the upper and lower transistor pairs. Typically, adding resistances into a transconductance circuit increases differential noise for the circuit. However, by coupling the impedance R1 between the upper and lower transistor pairs, noise that may be generated across the impedance R1 may be common mode noise shared by each of the first and second sets of paired transistors. Thus, no noise should be contributed by the impedance R1.

FIG. 7 illustrates an enhanced transconductance circuit 700, according to an embodiment of the present invention that combines the I-bridge circuit and the doublet circuit. By combining the I-bridge circuit and the doublet circuit, this embodiment improves transconductance linearity even further.

The enhanced transconductance circuit 700 of this embodiment may include two sets of differential transistor pairs QU1.1, QU1.2 and QL1.1, QL1.2, an impedance R1, and voltage followers FOLR.1, FOLR.2 of an I-bridge circuit. The circuit 700 also may include two sets of area offset differential transistor pairs QU2.1, QU3.1 and QU2.2, QU3.2; QL2.1, QL3.1 and QL2.2, QL3.2 of a doublet circuit. As illustrated, bases of the doublet transistors QU2.1, QU3.1, QL2.1, and QL3.1 may be coupled to outputs of the voltage follower FOLR.1. Similarly, bases of the doublet transistors QU2.2, QU3.2, QL2.2, and QL3.2 may be coupled to outputs of the voltage follower FOLR.2.

The doublet circuit may include current sources IU.1, IU.2, IL.1, IL.2 coupled between corresponding sets of doublet transistor emitters and source potentials VDD and VSS. The enhanced transconductance circuit 700 may have output terminals IOUTP.1, IOUTM.1, IOUTP.2, and IOUTM.2 coupled to collectors of transistors of each of the combined I-bridge circuit and the doublet circuit.

During operation, the enhanced transconductance circuit 700 improves linearity by combining the transconductance of the I-bridge circuit and doublet circuit. FIG. 8 is a graph 800 simulating a transconductance and differential output current IOUT for the enhanced transconductance circuit 700 having an area offset factor AOFF=6 versus the differential pair circuit 100 of FIG. 1. The output of each circuit type is normalized for comparative purposes. As illustrated in FIG. 8(a), the simulated transconductance linearity for the enhanced transconductance circuit 700 is improved over that of the differential pair circuit 100 over a range of differential input voltages VIN from approximately −50 mV to 50 mV.

The enhanced transconductance circuit 700 improves differential output current IOUT over that of the differential pair circuit 100. As illustrated in FIG. 8(b), the enhanced transconductance circuit 700 may generate an output current IOUT that tracks changes for the differential input voltage VIN without saturation. For example, the output current of the enhanced transconductance circuit 700 may track changes for differential input voltages VIN from approximately −200 mV to 200 mV without saturation. In contrast, the output current of the differential pair circuit 100, which is limited by the output current of the current source ISOURCE, begins to saturate as the differential input voltages VIN begin to diverge from 0 mV.

The enhanced transconductance circuit 700 also minimizes output error currents for common mode input voltages. In various embodiments, the output current may be configured to correspond to various ranges of differential input voltages VIN by changing the value of the common impedance R1. In various embodiments, the area offset factor AOFF may be configured to adjust the transconductance linearity for the enhanced transconductance circuit 700 for predetermined ranges of differential input voltages VIN.

FIG. 9 is a method 900 for generating a pair of output currents from a transconductance circuit which track voltage changes for a predetermined range of input voltages according to an embodiment of the present invention. As illustrated in block 910, the method 900 may apply one of a pair of input voltages across bases of a corresponding set of complementary I-bridge differential transistor pairs and corresponding sets of complementary doublet differential transistor pairs. The method 900 may apply the other of the pair of input voltages across opposite bases of the corresponding set complementary I-bridge differential transistor pairs and the corresponding sets of complementary doublet differential transistor pairs (block 920). The method 900 may generate the pair of output currents from a first and second pair of outputs of the transconductance circuit, wherein each output of each pair may represent one-half of one of the pair of output currents for the transconductance circuit (block 930).

In an embodiment, the method 900 may configure area offsets for the complementary sets of doublet differential transistor pairs to generate an approximately linear transconductance across the predetermined range of input voltages (block 902). In an embodiment, the method may configure a common impedance value for the I-bridge differential transistor pairs to generate the output current for the predetermined range of input voltages (block 904).

FIG. 10 is a diagram of a fully differential amplifier for use with embodiments of the present invention. FIG. 10A illustrates a fully differential op-amp 1010 symbolically. The op-amp 1010 may generate a pair of output voltages VOUTP, VOUTM based on a difference between a pair of input voltages VINP, VINM (e.g., (VOUTP−VOUTM)=A*(VINP−VINM), where ‘A’ may be the open loop gain of the op-amp 1010).

FIG. 10B provides a block diagram for the fully differential op-amp 1010. As illustrated, a GM circuit 1020 may generate differential output currents IOUTP1, IOUT1 in response to input voltages VINP, VINM (e.g., (IOUTP1−IOUTM1)=GM*(VINP−VINM)). Signal current mirrors 1030 may generate output currents IOUTP2, IOUTM2 corresponding to the currents IOUTP1, IOUTM1 received from the GM circuit 1020. The output currents IOUTP2, IOUTM2 may pass through impedance blocks 1040.1, 1040.2, which may create corresponding output voltages having magnitude GM*Z*(VINP−VINM). Amplifier buffers 1050.1, 1050.2 may generate output voltages VOUTP=−VOUTM (e.g., (VOUT−VOUTM)=GM*Z*(VINP−VINM)).

FIG. 10C illustrates application of the GM circuit 1020 as an input stage for the op-amp 1010. As illustrated, the GM circuit 1020 may generate complementary pairs of output currents IOUTP1/2 and IOUTM1/2, each representing half of the overall current for IOUTP1, IOUTM1. The signal current mirrors 1030 may be represented as complementary sets of mirrors 1030.1-1030.4, each receiving a respective input current signal and generating corresponding mirrored output currents. A first pair of output currents IOUTP2/2, IOUTM2/2 may be summed at an output node to generate the output current IOUTP and a second pair of output currents IOUTM2/2, IOUTP2/2 may be summed at an output node to generate the output current IOUTM.

Several embodiments of the present invention are specifically illustrated and described herein. However, it will be appreciated that modifications and variations of the present invention are covered by the above teachings. In other instances, well-known operations, components and circuits have not been described in detail so as not to obscure the embodiments. It can be appreciated that the specific structural and functional details disclosed herein may be representative and do not necessarily limit the scope of the embodiments.

Those skilled in the art may appreciate from the foregoing description that the present invention may be implemented in a variety of forms, and that the various embodiments may be implemented alone or in combination. Therefore, while the embodiments of the present invention have been described in connection with particular examples thereof, the true scope of the embodiments and/or methods of the present invention should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, specification, and following claims.

## Claims

1. A transconductance circuit, comprising:

first and second sets of differential transistor pairs, wherein within the first set, emitters of the transistors are coupled to a first common node and collectors of the transistors are coupled to a first pair of output terminals of the transconductance circuit, and wherein within the second set, emitters of the transistors are coupled to a second common node, and collectors of the transistors are coupled to a second pair of output terminals of the transconductance circuit, and wherein each set has a first transistor to receive a first input voltage at its base, and a second transistor to receive a second input voltage at its base; and
an impedance coupled between the first and second common nodes.

2. The transconductance circuit of claim 1, further comprising:

a first voltage follower to receive the first input voltage at a first input terminal and replicate the first input voltages across the bases of the first transistors of each set; and
a second voltage follower to receive the second input voltage at a second input terminal and replicate the second input voltage across the bases of the second transistors of each set.

3. The transconductance circuit of claim 2, wherein the circuit is configured to generate output currents from each output terminal that track changes for the first and second input voltages across a predetermined voltage range.

## Patent History

Publication number: 20140159813
Type: Application
Filed: Feb 18, 2014
Publication Date: Jun 12, 2014
Applicant: ANALOG DEVICES, INC. (Norwood, MA)
Inventor: Sandro HERRERA (Medford, MA)
Application Number: 14/182,799

## Classifications

Current U.S. Class: Including Differential Amplifier (330/252)
International Classification: H03F 3/45 (20060101);