GB2329774A - A transconductance amplifier with a V-I converter and a diode load for producing a logarithmic output which is then exponentiated to give a linear output - Google Patents

Abstract

A bipolar OTA having an improved transconductance linearity is provided, which is comprised of a V-I converter 1, at least a first load diode (and a second D2 in a differential arrangement), and an output circuit 31. The V-I converter receives an input voltage and produces an output current according to the received input voltage. The first load diode converts logarithmically the output current of the V-I converter to an output voltage. The output circuit exponentially expands the output voltage of the first load diode, thereby producing an output of the OTA. The transconductance characteristic of the output circuit is adjustable by means of control voltage Vc or by varying an emitter area ratio K. As the output circuit, (a) a triple-tail cell having emitter-coupled first, second, and third bipolar transistors driven by a single common tail current, (b) a quadritail cell having emitter-coupled first, second, third, and fourth bipolar transistors driven by a single common tail current, or (c) two cross-coupled, emitter-coupled unbalanced differential pairs is preferably used. When the V-I converter has an incompletely-linear transconductance characteristic, the total transconductance characteristic of the OTA may be linearized by adjusting the transconductance of the output circuit.

Description

OPERATIONAL TRANSCONDUCTANCE AMPLIFIER BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a differential amplifier circuit and more particularly, to a bipolar operational transconductance amplifier comprised of a voltage-to-current (V-I) converter with a load diode and an output circuit, which has an improved transconductance linearity within an input voltage range as wide as approximately 1 V or greater and which is suitable for a semiconductor integrated circuit (IC).

2. Description of the Prior Art A differential amplifier circuit having a superior trans conductance linearity within a comparatively wide input voltage range has been known as an "Operational Transconductance Amplifier (OTA)".

A conventional bipolar OTA is shown in Fig. 1, which is termed the "Gilbert gain cell". This conventional OTA is disclosed in IEEE Journal of Solid-State Circuits, Vol. SC-3, No.

4, pp. 353-365, December 1968, which was written by B. Gilbert.

As shown in Fig. 1, a first balanced differential pair is formed by two npn-type bipolar transistors Q101 and Q102. An emitter of the transistor Q101 is connected to one terminal of a constant current sink 101 sinking a constant current Io. An emitter of the transistor Q102 is connected to one terminal of another constant current sink 102 sinking the same constant current Ic as the constant current sink 101 for the transistor Q101. The other terminals of the two constant current sinks 101 and 102 are connected to the ground. These two transistors Q101 and 0102 are driven by the current sinks 101 and 102, respectively.

The emitters of the transistors Q101 and Q102 are coupled together through a common emitter resistor 104 having a resistance R. The resistor 104 serves as an emitter-degeneration resistor.

A differential input voltage VIN as an input signal to the conventional OTA is applied across bases of the transistors Q101 and Q102.

The transistors Q101 and 0102, the constant current sinks 101 and 102, and the emitter resistor 104 serves as aV-I converter.

Two diode-connected npn-type bipolar transistors Q103 and Q104 are provided as loads of the transistors Q101 and Q102, respectively. Specifically, emitters of the transistors Q103 and Q104 are connected to collectors of the transistors Q101 and Q102, respectively. Abase and a collector of the transistor Q103 are coupled together to be connected to a power supply line (not shown) applied with a power supply voltage Vcc. A base and a collector of the transistor Q104 are coupled together to be connected to the same power supply line of Vcc.

A second balanced differential pair is formed by two npn-type bipolar transistors Q105 and Q106. Emitters of the transistors Q105 and Q106 are coupled together to be connected to one terminal of a constant current sink 103 sinking a constant current I1. The other terminal of the constant current sink 103 is connected to the ground. Bases of the transistors Q105 and Q106 are connected to the collectors of the transistors Q102 and Q101 serving as output terminals of the first balanced differential pair, respectively.

Here, a differential output current AIc, which is an amplified output signal of the conventional OTA, is defined as the difference between collector currents Icios and Icy06 of the transistors Q105 and Q106, i.e., tIc = Ictos - 1Ct06. Then, the differential output current Aic is derived from the collectors of the transistors Q105 and Q106.

Next, the operation of the Gilbert gain cell shown in Fig.

1 is explained below.

Here, supposing that the base-widthodulation (i.e., the Early voltage) is ignored and that the common-base current gain factor of a bipolar transistor is equal to unity, a collector current 1c of a bipolar transistor is typically given as the following expression (la).

In the expression (la), vBE is a base-to-emitter voltage of the bipolar transistor, and Isis a saturation current thereof.

Also, VT is the thermal voltage defined as VT = kT/q, where k is the Boltzmann's constant, T is absolute temperature in degrees Kelvin, and q is the charge of an electron The expression (la) can be rewritten to the following form (lb).

The form (lob) means that the base-to-emitter voltage VBE is given by logarithmically compressing the collector current Ic.

When the differential input voltage VIN is applied across the bases of the transistors Q101 and Q102 of the first balanced differential pair, the following relationship (2) is established around the loop consisting of the input voltage Vrw and the two base-emitter junctions of the transistors Q101 and Q102 according to the Kirchhoff's voltage law.

VIN = VBE101 - VBE102 + Ri (2) In the relationship (2), VEE101 and VBE102 are base-toemitter voltages of the transistors Q101 and Q102, respectively, and i is a current flowing through the common emitter resistor 104.

Supposing that a relationship of (R.i) > > (V3E101 - VBE102) is established, the current i is expressed as the following equation (3) using the relationship (2).

The equation (3) means that the current i is approximately proportional to the applied differential input voltage VN.

Fig. 2 shows the transfer characteristic of the first differential pair of the transistors QiOl and Q102 with the emitter resistor 104, where the product (R.i) of the resistance R of the emitter resistor 104 and the current i flowing therethrough is set as 1 volt.

As seen from Fig. 2, collector currents (i.e., differential output currents) IC101 and IC102 of the first differential pair are approximately proportional to the differential input voltage VIN. In other words, the trans conductance of the first differential pair is approximately linear.

The current i flowing through the emitter resistor 104 further flows through the diode-connected transistors Q103 and Q104 as differential currents. Thus, the collector currents idiot and IC102 are expressed as the following equations (4a) and (4b), respectively. clol= Io+ i (4a) IC102 = I0 - i (4b) Therefore, the following relationships (5a) and (5b) are established using the above expression (1b).

Thus, from the relationships (5a) and (Sb), the voltage difference AVBE, which is defined as the difference between the base-to-emitter voltages VBE101 and VBE102, is given by the following expression (6).

It is seen from the expression (6) that the voltage difference #VBE is in a logarithmically compressed form of the collector currents IC101 and Ico. This means that the voltage difference AV96 is logarithmically proportional to the collector currents IC101 and 1C1O2 (i.e., the differential output currents of the first differential pair).

The voltage difference AVa is then applied across the bases of the transistors Q105 and Q106 of the second balanced differential pair and then, it is amplified therein. Thus, the differential output current Aic of the second balanced differential pair, which is an amplified output signal of AV9E, is given as the following expression (7).

The expression (7) is obtained by the known result that a differential output current hI of a balanced differential pair of two emitter-coupled bipolar transistors driven by a constant current I, is expressed as

where Vi is a differential input voltage applied across the bases of the two bipolar transistors.

It is seen from the relationship (7) that the differential output current Aic of the second differential pair is in an exponentially expanded (i.e., logarithmically inverted) form of the applied voltage difference AvaE The above relationship (7) is rewritten to the following expression (8a) by removing the term (#VBE/VT) with the use of the above expression (6).

This expression (8a) can be further rewritten to the follows expression (8b) using the identity of tanh x = (ex - eX)/(ex + ex).

Thus, it is seen from the expression (8b) that the differential output current AIc of the conventional bipolar OTA shown in Fig. 1 is proportional to the current i flowing through the emitter resistor 104. This means that the current i can be derived from the collectors of the transistors Q105 and Q106. On the other hand, as described previously with reference to the expression (3), the current i is approximately proportional to the applied differential input voltage VIN.

Accordingly, the differential output current AIc is approximately proportional to the differential input voltage V1N.

In other words, the circuit configuration shown in Fig. 1 has an approximately linear transconductance and is capable of an OTA function.

With the conventional Gilbert gain cell in Fig. 1, using the above expression (8b), the collector currents Icios and Iclo of the transistors Q105 and Q106 can be expressed as the following equations (9a) and (9b), respectively.

On the other hand, from the above relationships (4a) and (4b), the collector currents 10102 and Icioz of the transistors Q101 and Q102 are expressed as

Therefore, it is seen fromthe equations (9a), (9b), (10a), and (lOb) that the collector currents Icios and It106 of the transistors Q105 and Q106 are equal to the results obtained by simply multiplying the collector currents Icioi and Icy02 by the term (I1/2Io) respectively. This means that the trans conductance non-linearity of the first differential pair of the transistors Q101 and Q102 is not improved by the logarithmic compression and exponential expansion in the Gilbert gain cell shown in Fig. 1. Thus, there is the need to improve the transconductance linearity of the Gilbert gain cell.

Further, the conventional Gilbert gain cell contains the arithmetic approximation as shown in the above equation (3).

Therefore, unless the value of the resistance R of the emitter resistor 104 and the values of the constant currents Io and I1 are suitably designed or optimized, no satisfactory transconductance linearity is practically realized. In other words, no completely linear transconductance characteristic is able to be realized by the Gilbert gain cell.

As seen from Fig. 2, the collector currents Iclol and Iclo2 of the transistors Q101 and Q102 of the first differential pair are not correctly proportional to the differential input voltage VIN within the input voltage range of ii V. This means that the transconductance characteristic of the Gilbert gain cell is not completely linear within the input voltage range of i1 V.

An OTA is an essential, basic function block in analog signal applications. In recent years, there has been the strong need of improving the transconductance linearity of OTAs.

SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to provide a bipolar OTA having an improved transconductance linearity.

Another object of the present invention is to provide a bipolar OTA having a completely linear -transconductance characteristic within a specific input voltage range.

Still another object of the present invention is to provide a bipolar OTA having a completely linear trans conductance characteristic within an input voltage range as wide as approximately ii V or greater.

The above objects together with others not specifically mentioned will become clear to those skilled in the art from the following description.

A bipolar OTA according to the present invention is comprised of a V-I converter, a first load diode, and an output circuit.

The V-I converter receives an input voltage and produces an output current according to the received input voltage.

The first load diode converts logarithmically the output current of the V-I converter to an output voltage.

The output circuit exponentially expands the output voltage of the first load diode, thereby producing an output of the OTA. The output circuit is capable of tuning its transconductance characteristic.

With the bipolar OTA according to the present invention, the V-I converter produces the output current according to the received input voltage and then, the first load diode converts logarithmically the output current of the V-I converter to an output voltage. Further, the output circuit, which is capable of tuning its trans conductance characteristic, exponentially expands the output voltage of the first load diode, thereby producing the output of the OTA.

Therefore, even if the transconductance of the V-I converter is not completely linear, the transconductance non linearity of the V-I converter is able to be improved by adjusting the transconductance characteristic of the output circuit to cancel the transconductance non-linearity of the V-I converter.

Accordingly, the bipolar OTA according to the present invention has an improved transconductance linearity.

If the transconductance non-linearity of the V-I converter is canceled by adjusting the trans conductance characteristic of the output circuit, the bipolar OTA according to the present invention has a completely linear trans conductance characteristic.

In a preferred embodiment of the OTA according to the present invention, the output circuit includes emitter-coupled first, second, and third bipolar transistors driven by a common tail current. The output voltage of the first load diode is applied across bases of the first and second transistors. The output of the OTAis derived from collectors of the first and second transistors. A control voltage is applied to a base of the third transistor for tuning transconductance of the output circuit.

In this case, the output circuit constitute a tripletail cell capable of realizing a completely linear transconductance characteristic. As a result, if the V-I converter has a completely linear trans conductance characteristic, the bipolar OTA according to the present invention is able to have a completely linear trans conductance characteristic within a specific input voltage range.

It is preferred that the first and second transistors of the output circuit have a same emitter area and the third transistor of the output circuit has an emitter area K times as large as that of the first and second transistors, where K is a constant greater than unity.

There is an additional advantage that the adjustment of the transconductance characteristic of the output circuit (i.e., the triple-tail cell) is facilitated, because the transconductance characteristic of the output circuit is tuned not only by the control voltage but also by the constant K.

In another preferred embodiment of the OTA according to the present invention, the output circuit includes emittercoupled first, second, third, and fourth bipolar transistors driven by a common tail current. The output voltage of the first load diode is applied across bases of the first and second transistors. The output of the OTA is derived from collectors of the first and second transistors. A control or tuning voltage is commonly applied to bases of the third and fourth transistors for changing a transconductance of the output circuit.

In this case, the output circuit constitute a quadritail cell capable of realizing a completely linear trans conductance characteristic. As a result, if the V-I converter has a completely linear trans conductance characteristic, the bipolar OTA according to the present invention is able to have a completely linear trans conductance characteristic within a specific input voltage range.

It is preferred that the first and second transistors of the output circuit have a same emitter area and the third and fourth transistors of the output circuit have a same emitter area (K/2) times as large as that of the first and second transistors, where K is a constant greater than unity.

There is an additional advantage that the adjustment of the transconductance characteristic of the output circuit (i.e., the quadritail cell) is facilitated, because the transconductance characteristic of the output circuit is tuned not only by the control voltage but also by the constant K. Further, there is an additional advantage that the output circuit performs a class-A operation.

In still another preferred embodiment of the OTA according to the present invention, the output circuit includes a first unbalanced differential pair of emitter-coupled first and second bipolar transistors driven by a first common tail current and a second unbalanced differential pair of emitter-coupled third and fourth bipolar transistors driven by a second common tail current. The second transistor has an emitter area K times as large as that of the first transistor, where K is a constant greater than unity. The third transistor has an emitter area K times as large as that of the fourth transistor. Bases of the first and third transistors are coupled together. Bases of the second and fourth transistors are coupled together. Collectors of the first and third transistors are coupled together.

Collectors of the second and fourth transistors are coupled together.

The output voltage of the first load diode is applied across the coupled bases of the first and third transistors and the coupled bases of the second and fourth transistors. The output of the OTA is derived from the coupled collectors of the first and third transistors and the coupled collectors of the second and fourth transistors.

In this case, the trans conductance characteristic of the output circuit is changed by the constant K.

In a further preferred embodiment of the OTA according to the present invention, the V-I converter has a completelylinear transconductance characteristic within a specific range of the differential input voltage.

In this case, there is an additional advantage that the transconductance of the bipolar OTA is completely linear by simply tuning the trans conductance characteristic of the output circuit to be completely linear.

In a still further preferred embodiment of the OTA according to the present invention, a second load diode is provided to be cascode-connected to the first load diode. In this case, a completely linear trans conductance characteristic of the OTA is realized.

BRIEF DESCRIPTION OF THE DRAWINGS In order that the present invention may be readily carried into effect, it will now be described with reference to the accompanying drawings.

Fig. 1 is a circuit diagram of a conventional bipolar OTA termed the Gilbert gain cell.

Fig. 2 is a graph showing the transfer characteristic of the first differential pair with the emitter resistor in the conventional bipolar OTA shown in Fig. 1.

Fig. 3 is a circuit diagram of a bipolar OTA according to a first embodiment of the present invention.

Fig. 4 is a circuit diagram of a bipolar OTA according to a second embodiment of the present invention.

Fig. S is a circuit diagram of a bipolar V-I converter used for the bipolar OTA according to the present invention, which has a completely-linear transfer characteristic.

Fig. 6 is a circuit diagram of a bipolar OTA according to the second embodiment of Fig. 4, in which a same circuit configuration as that of the conventional OTA shown in Fig. 1 is used for the V-I converter.

Fig. 7 is a graph showing the transconductance characteristic of the triple-tail cell of the bipolar OTA according to the first and second embodiments shown in Figs. 8 and 6, in which the transconductance characteristic is tunable by changing the constant a.

Fig. 8 is a circuit diagram of a bipolar OTA according to the first embodiment of Fig. 3, in which a same circuit configuration as that of the conventional OTA shown in Fig. 1 is used for the V-I converter.

Fig. 9 is a graph showing the transfer characteristic of the bipolar OTA according to the first embodiment of Fig. 8.

Fig. 10 is a circuit diagram of a bipolar OTA according to a third embodiment of the present invention.

Fig. 11 is a circuit diagram of a bipolar OTA according to a fourth embodiment of the present invention.

Fig. 12 is a circuit diagram of a bipolar OTA according to the fourth embodiment of Fig. 11, in which a same circuit configuration as that of the conventional OTA shown in Fig. 1 is used for the V-I converter.

Fig. 13 is a graph showing the transfer characteristic of the bipolar OTA according to the fourth embodiment of Fig. 12.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will be described in detail below while referring to the drawings attached.

FIRST EMBODIMENT A bipolar OTA according to a first embodiment of the present invention is shown in Fig. 3.

As shown in Fig. 3, this bipolar OTA is comprised of a V-I converter 1, two load diodes D1 and D2 for the V-I converter 1, a triple-tail cell 31 serving as an output circuit of the V-I converter 1.

The V-I converter 1 receives a differential input voltage VIN at its input terminals T1 and T2 and produces two differential output currents It and I according to the applied input voltage VIN at its output terminals T3 and T4. Cathodes of the load diodes D1 and D2 are connected to the output terminals T3 and T4 of the V-I converter 1, respectively. Anodes of the load diodes D1 and D2 are connected to a power supply line (not shown) applied with a power supply voltage V=.

The triple-tail cell 31 includes three npn-type bipolar transistors Q1, Q2, and Q3 whose emitters are coupled together and a constant current sink 2 sinking a constant current 1E The coupled emitters of the transistors Q1, Q2, and Q3 are connected to the ground through the constant current sink 2. The transistors Q1, Q2, and Q3 are driven by the common tail current IE- The emitter areas of the transistors Q1 and Q2 are equal to each other. The emitter area of the transistor Q3 is K times as large as that of the transistors Q1 and Q2, where K is a constant greater than unity. The transistors Qi and Q2 maybe simply formed by unit bipolar transistors.

Bases of the transistors Q1 and Q2, which serve as input terminals of the triple-tail cell 31, are connected to the output terminals T3 and T4 of the V-I converter 1 (i.e., the cathodes of the load diodes D1 and D2). A voltage difference AV, which is equal to the difference between the differential output voltages generated by converting the differential output currents I' and I- to voltages, is applied across the bases of the transistors Q1 and Q2.

A base of the transistor Q3, which serves as a control terminal of the triple-tail cell 31, is applied with a control voltage Vc.

Collectors of the transistors Q1 and Q2 serve as output terminals of the triple-tail cell 31, from which a differential output current Al of the bipolar OTA is derived. The differential output current is defined as the difference between collector currents Icl and 102 of the transistors Q1 sand Q2, i.e., Al = Ici - 102.

A collector of the transistor Q3 is directly connected to the power supply line of Vcc.

Next, the operation of the bipolar OTA according to the first embodiment is explained below.

First, it is supposed that the differential output currents I+ and I of the V-I converter 1 are expressed by the following equations (11) and (12), respectively. t=10+G0 V (11) I+=Io- G0VIN (12) In the equations (11) and (12), Io and Go are a constant current and a conductance of the V-I converter 1, respectively.

The differential output currents I+ and I- are logarithmically compressed by the load diodes Dl and D2 to produce differential output voltages, respectively. The differential output voltages thus produced are equal to the inter-terminal voltages of the load diodes D1 and D2, respectively.

Each of the inter-terminal voltages of the load diodes Dl andD2 is given by the previously-explained equation (1b), where Ic is replaced with I+ or I-. Thus, the voltage difference AV is expressed by the following equation (13).

It has been known that the differential output current Al of the triple-tail cell 31 is given by the following equation (14).

Substituting the equation (13) into the equation (14) gives the following equation (15).

In the equation (15), the constant a is given as the following expression (16).

If the control voltage Ve and the emitter area ratio K are set to satisfy the relationship of a 1, the denominator of the equation (15) becomes approximately equal to unity. As a consequence, the differential output current Awl is approximated to the following equation (17).

It is seen from the equation (17) that the differential output current Al of the OTA according to the first embodiment is approximately proportional to the differential input voltage V. In other words, the circuit configuration shown in Fig. 3 realizes an OTA function.

With the bipolar OTA according to the first embodiment of the present invention, as explained above, the differential output current If and I of the V-I converter 1 are converted to the inter-terminal voltages of the load diodes D1 and D2 and then, the voltage difference AV between these inter-terminal voltages is applied across the input terminals of the triple-tail cell 31 serving as the output circuit of the V-I converter 1. The triple-tail cell 31 is capable of changing or tuning its trans conductance characteristic by adjusting at least one of the control voltage Vc and the emitter area ratio K.

Therefore, even if the trans conductance characteristic of the V-I converter 1 is not completely linear, the trans conductance non-linearity of the V-I converter 1 is able to be decreased or canceled by adjusting the transconductance characteristic of the triple-tail cell 31 to cancel the transconductance non-linearity of the V-I converter 1.

Accordingly, the bipolar OTA according to the first embodiment has an improved transconductance linearity.

Also, the bipolar OTA according to the first embodiment has a linear trans conductance within a specific range of the differential input voltage Viw.

As the V-I converter 1 shown in Fig. 3, a c transistor Q5 is further connected to the ground through a constant current sink 4 sinking the same constant current 1o as the constant current sink 4.

A collector of the transistor Q4 is connected to the power supply line of Vce through the lode diode D1. A collector of the transistor Q5 is connected to the power supply line of Vce through the lode diode D2.

A base of the transistor Q4 is connected to the input terminal T1 and a base of the transistor Q5 is connected to the input terminal T2. The differential input voltage VIN is applied across the bases of the transistors Q4 and Q5.

A current i will flow through the emitter resistor 5 according to the value of the differential input voltage VIN.

In the bipolar OTA shown in Fig. 8, as explained in the conventional bipolar OTA of Fig. 1, the transconductance value of the triple-tail cell 31 decreases non-linearly with the increasing amplitude of the applied voltage difference AV due to the non-linearity of the V-I converter 1.

On the other hand, if the values of the emitter area ratio K and the control voltage Ve are determined so that the value of the constant a shown in the equation (16) is greater than unity (i.e., a > 1), the transconductance value of the triple-tail cell 31 increases non-linearly with the increasing amplitude of the voltage difference AV.

Fig. 7 shows the transconductance characteristic of the triple-tail cell 31. As seen from Fig. 7, the transconductance characteristic of the triple-tail cell 31 can be changed or adjusted by tuning the value of the constant a.

Accordingly, the decrease of the trans conductance value of the V-I converter 1 is able to be decreased by the increase of the transconductance value of the triple-tail cell 31, thereby improving the total trans conductance characteristic of the bipolar OTA according to the first embodiment of Fig. 3.

Fig. 9 shows the total transconductance characteristic of the OTA according to the first embodiment shown in Fig. 8, where Rel0 = 2 V and a = 1.25.

It is seen from Fig. 9 that the circuit configuration shown in Fig. 8 has a completely-linear transconductance characteristic when the differential input voltage VZN is within the range of O to approximately il.2 V.

SECOND EMBODIMENT A bipolar OTA according to a second embodiment of the present invention is shown in Fig. 4.

As shown in Fig. 4, this bipolar OTA has the same circuit configuration as that of the OTA according to the first embodiment except that the load diode D1 is replaced with two cascodeconnected load diodes Dli and D12 the load diode D2 is replaced with two cascode-connected load diodes D13 and D14. Therefore, explanation about the same configuration as that of the first embodiment is omitted here by attaching the same reference symbols as those of the first embodiment in Fig. 4 for the sake of simplification of description.

The cascode-connected load diodes D11 and D12 are connected to the output terminal T3 of the V-I converter 1 and the power supply line of Vcc- The cascode-connected load diodes D13 and D14 are connected to the output terminal T4 of the V-I converter 1 and the power supply line of V=.

The inter-terminal voltage of the diodes Dll and D12 is twice as large as that of the load resistor D1 in the first embodiment. Similarly, the inter-terminal voltage of the diodes D13 and D14 is twice as large as that of the load resistor D2 in the first embodiment. Therefore, the differential output current Al of the OTA according to the second embodiment of Fig.

4 is given by the following equation (18).

The equation (18) is rewritten to the following equation (19) by substituting the above-described equation (13) into the equation (18).

In the equation (19), the constant K relating to the emitter area ratio of the transistor Q3 is set to satisfy the following relationship (20).

If the value of K is set as 2 in the expression (20), the control voltage Vc will be zero. This means that the control voltage Ve may be equal to the input common mode voltage, which produces an additional advantage of simplification of the circuit configuration.

It is seen from the equation (19) that the differential output current Al is correctly proportional to the differential input voltage VTN. In other words, the circuit configuration shown in Fig. 4 realizes a completely linear OTA function if the transconductance of the V-I converter 1 is completely linear.

With the bipolar OTA according to the second embodiment of Fig. 4, if the transconductance of the V-I converter 1 is completely linear, there is an advantage that this OTA has a completely-linear transconductance characteristic in addition to the same advantages as those of the first embodiment.

An example of the V-I converter 1 having a completely-linear transconductance characteristic is shown in Fig. 5. It is needless to say that the circuit configuration shown in Fig. 5 may be used for the V-I converter 1 in the OTAs according to the first embodiment of Fig. 3 and any other embodiments described later in this specification.

The V-I converter 1 shown in Fig. 5 includes a balanced differential pair of npn-type bipolar transistors Qil and Q12 whose emitter areas are equal to each other. Emitters of the transistors Q11 and Q12 are coupled together through an emitter resistor 15 having a resistance R. The emitter of the transistor Q11 is further connected to the ground through an emitterfollower-augmented current mirror circuit 41. The emitter of the transistor Q12 is further connected to the ground through an emitter-follower-augmented current mirror circuit 42.

The current mirror circuits 41 and 42 serve as variable current sources for the transistors Q11 and Q12, respectively.

The differential output currents Ifi and I- of the V-I converter 1 are derived through the current mirror circuits 41 and 42, respectively.

A collector of the transistor Q11 is connected to the power supply line of Vccthrough a constant current source 11 supplying a constant current Io. The transistor Q11 is driven by the constant current lo. A collector of the transistor Q12 is connected to the power supply voltage of Vcc through a constant current source 12 supplying the same constant current Io. The transistor Q12 is driven by the constant current Io.

A base of the transistor Qil is connected to the input terminal Tl and a base of the transistor Q12 is connected to the input terminal T2. The differential input voltage VIN is applied across the bases of the transistors Q11 and Q12.

A current i will flow through the emitter resistor 15 according to the value of the differential input voltage VIN.

The current mirror circuit 41 is comprised of two npn-type bipolar transistors Q13 and Q14 whose bases are coupled together, an npn-type bipolar transistor Q15 serving as an emitter-follower transistor, and a constant voltage source 13 supplying a constant voltage VLS A collector of the transistor Q13 is connected to the emitter of the transistor Qll. An emitter of the transistor Q13 is directly connected to the ground. The coupled bases of the transistors Q13 and Q14 are connected to a negative electrode of the voltage source 13. An emitter of the transistor Q14 is directly connected to the ground. A base of the transistor Q15 is connected to the collector of the transistor Q11. A collector of the transistor Q15 is directly connected to the power supply line of Vcc. An emitter of the transistor Q15 is connected to the positive electrode of the voltage source 13. The constant voltage source 13 serves to shift the voltage level at the coupled bases of the transistors Q13 and Q14. The differential output current I- is derived from a collector of the transistor Q14.

Similarly, the current mirror circuit 42 is comprised of two npn-type bipolar transistors Q16 and Q17 whose bases are coupled together, an npn-type bipolar transistor Q18 serving as an emitter-follower transistor, and a constant voltage source 14 supplying the same constant voltage VLS as that of the voltage source 13.

A collector of the transistor Q16 is connected to the emitter of the transistor Q12. An emitter of the transistor Q16 is directly connected to the ground. The coupled bases of the transistors Q16 and Q17 are connected to a negative electrode of the voltage source 14. An emitter of the transistor Q17 is directly connected to the ground. A base of the transistor Q18 is connected to the collector of the transistor Q12. A collector of the transistor Q18 is directly connected to the power supply line of Vcc. An emitter of the transistor Q18 is connected to the positive electrode of the voltage source 14. The constant voltage source 14 serves to shift the voltage level at the coupled bases of the transistors Q16 and Q17. The differential output current I+ is derived from a collector of the transistor Q14.

With the completely-linear V-I converter 1 shown in Fig.

5, the transistors Q11 and 412 of the differential pair are driven by the same constant currents lo. Therefore, base-to-emitter voltages and of the transistors 011 and 012 are equal to each other.

Thus, the current i flowing through the emitter resistor 15 is expressed by the following equation (21).

(21) R Unlike the previously-described equation (3) in the conventional OTA shown in Fig. 1, the equation (21) contains no arithmetic approximation.

Accordingly, the differential output currents I+ and I of the V-I converter 1, which are outputted from the current mirror circuits 41 and 42, are given by the following expressions (22a) and (22b), respectively, where Go = 1/k.

It is clearly seen from the equations (22a) and (22b) that the differential output currents I+ and I- are correctly proportional to the differential input voltage :N With the V-I converter shown in Fig. 5, the transistors Qil and Q12 constituting the differential pair are respectively driven by the corresponding constant current sources 11 and 12, respectively. Therefore, the voltage applied across the resistor 15 is equal to the differential input voltage WN, which means that the resistor 15 is equivalent to a "floating resistor".

As a result, a completely or perfectly linear conversion operation is realized within a specific range of the differential input voltage VXN with a simple circuit configuration.

In the V-I converter 1 shown in Fig. 5, the linearity of the V-I conversion operation is determined by only the linearity of resistance R of the emitter resistor 15.

Instead of the circuit configuration shown in Fig. 5, the circuit configuration disclosed in the Japanese Non-examined Patent Publication No. 9-116350 published in 1997 may be used for the completely-linear V-I converter 1.

It is needless to say that a same circuit configuration as that of the conventional OTA shown in Fig. 1 may be used as the V-I converter 1, the entire circuit configuration of which is shown in Fig. 6.

THIRD EMBODIMENT Fig. 10 shows abipolar OTA according to a third embodiment of the present invention, which is a variation of the first embodiment shown in Fig. 3. A quadritail cell 32 is provided instead of the triple-tail cell 31.

The npn-type transistor Q3 having the emitter area ratio K in the triple-tail cell 31 is equivalent to the combination of two npn-type bipolar transistors Q3A and Q3B having the emitter area ratio (K/2). Therefore, the transistors Q3A and Q3B having the emitter area ratio (K/2) are provided instead of the transistor Q3 in the triple-tail cell 31.

Emitters of the transistors Q3A and Q3B are connected to the coupled emitters of the transistors Q1 and Q2. Bases of the transistors Q3A and Q3B are commonly applied with the control voltage Vc. Collectors of the transistors Q3A and Q3B are connected to the collectors of the transistors Qi and Q2, respectively.

Additionally, load resistors 6 and 7 having the same resistance RL are provided for the quadritail cell 32. The load resistor 6 is connected to the collector of the transistor Q1 and the power supply line, The load resistor 7 is connected to the collector of the transistor Q2 and the power supply line. An output voltage VOUT of the OTA is derived from output terminals T5 and T6 connected to the collectors of the transistors Ql and Q2.

In the bipolar OTA according to the third embodiment shown in Fig. 10, there is an additional advantage that the quadritail cell 32 realizes a class-A amplification operation in addition to the same advantages as those of the first embodiment. This is because a current flows through the transistors Q3A and Q3B even at AV = 0.

FOURTH EMBODIMENT Fig. 11 shows a bipolar OTA according to a fourth embodiment of the present invention, in which the combination of a first unbalanced differential pair of npn-type bipolar transistors Q21 and Q22 and a second unbalanced differential pair of npn-type bipolar transistors Q23 and Q24 is provided instead of the triple-tail cell 31 in the OTA according to the first embodiment shown in Fig. 3. The other circuit configuration is the same as that of the first embodiment.

In the first unbalanced differential pair, the transistor Q22 has an emitter area K times as large as that of the transistor Q21. Emitters of the transistors Q21 and Q22 are coupledtogether to be connected to the ground through a constant current sink 21 sinking a constant current 1.

In the second unbalanced differential pair, the transistor Q23 has an emitter area K times as large as that of the transistor Q24. Emitters of the transistors Q23 and Q24 are coupled together to be connected to the ground through a constant current sink 22 sinking a same constant current Its as the constant current sink 21.

Bases of the transistors Q21 and Q23 are coupled together to be connected to the output terminal T4 of the V-I converter 1. Bases of the transistors Q22 and Q24 are coupled together to be connected to the output terminal T3 of the V-I converter 1.

The voltage difference AV is applied across the coupled bases of the transistors Q21 and Q23 and those of the transistors Q22 and Q24.

Collectors of the transistors Q21 and Q23 are coupled together. Collectors of the transistors Q22 and Q24 are coupled together. The differential output current Al of the bipolar OTA is derived from the coupled collectors of the transistors Q21 and Q23 and those of the transistors Q22 and Q24. The differential output current Al is defined as #I = (IC21 + IC23) - (IC23 + IC24), where IC2lt IC22 IC23, and 1024 are collector currents of the transistors Q21, Q22, Q23, and Q24, respectively.

If the differential output currents of the first and second differential pairs are defined as Ali (= C21 - It22) and AI2(= IC23 - IC24), respectively, it has been known that #I1 and dI2 are given by the following equations (23a) and (23b), respectively.

In the equations (23a) and (23b), VK is an offset voltage defined by the following equation (24).

Vi:=Vrln(K) (24) Accordingly, the differential output current Al of the OTA is given by the following equation (25).

Therefore, the following equation (26) is obtained by using the expression (24).

On the other hand, if the value of the left side of the equation (26) is equal to 1, the equation (25) is rewritten to the following equation (27).

The equation (27) can be further written to the following equation (28).

As seen from the equation (28), the differential output current Al of the bipolar OTA according to the fourth embodiment is correctly proportional to the differential input voltage VIN if the value of the left side of the equation (26) is equal to 1. In other words, the OTA according to the fourth embodiment has a completely linear trans conductance characteristic if the V-I converter 1 has a circuit configuration capable of realizing a completely linear trans conductance characteristic such as the configuration shown in Fig. 5.

However, when a same circuit configuration as that of the conventional OTA shown in Fig. 1 is used as the V-I converter 1, as shown in Fig. 12, the V-I converter 1 has a non-linear transconductance characteristic as shown in Fig. 2. Therefore, even if the value of the left side of the equation (26) is equal to unity, a completely linear transconductance characteristic is not realized.

When the value of the left side of the equation (26) is greater than unity, the transconductance value of the crosscoupled, emitter-coupled differential pairs 33 increases nonlinearly with the increasing amplitude of the applied voltage difference AV due to the non linear operation of the first and second differential pairs. On the other hand, the trans conductance value of the V-I converter 1 decreases nonlinearly with the increasing amplitude of the voltage difference Av.

Accordingly, the decrease of the trans conductance value of the V-I converter 1 is able to be decreased by the increase of the transconductance value of the first and second differential pairs 33, thereby improving the total trans conduct ance characteristic of the bipolar OTA according to the fourth embodiment of Fig. 12.

Fig. 13 shows the total trans conductance characteristic of the OTA according to the fourth embodiment shown in Fig. 12, where R.I0 = 1 V and K - 5/4 (= 1.25).

It is seen from Fig. 13 that the circuit configuration shown in Fig. 12 has a completely-linear transconductance characteristic when the differential input voltage VIN is within the range of O to approximately iO.95 V.

While the preferred forms of the present invention have been described, it is to be understood that modifications will be apparent to those skilled in the art without departing from the scope of the invention, as determined by the following claims.

Each feature disclosed in this specification (which term includes the claims) and/or shown in the drawings may be incorporated in the invention independently of other disclosed and/or illustrated features.

Statements in this specification of the "objects of the invention" relate to preferred embodiments of the invention, but not necessarily to all embodiments of the invention falling within the claims.

The description of the invention with reference to the drawings is by way of example only.

The text of the abstract filed herewith is repeated here as part of the specification.

A bipolar OTA having an improved trans conductance linearity is provided, which is comprised of a V-I converter, a first load diode, and an output circuit. The V-I converter receives an input voltage and produces an output current according to the received input voltage. The first load diode converts logarithmically the output current of the V-I converter to an output voltage. The output circuit exponentially expands the output voltage of the first load diode, thereby producing an output of the OTA. The output circuit is capable of tuning its transconductance characteristic. As the output circuit, (a) a triple-tail cell having emitter-coupled first, second, and third bipolar transistors driven by a single common tail current, (b) a quadritail cell having emitter-coupled first, second, third, and fourth bipolar transistors driven by a single common tail current, or (c) two cross-coupled, emitter-coupled unbalanced differential pairs is preferably used. When the V-I converter has a completely-liner trans conductance characteristic, the total transconductance characteristic of the OTA is completely linear within a differential input voltage of approximately Al V.

Claims (19)

1. What is claimed is: 1. An operational transconductance amplifier comprising: (a) a V-I converter for receiving an input voltage and for producing an output current according to said received input voltage; (b) a first load diode for converting logarithmically said output current of said V-I converter to an output voltage; and (c) an output circuit for exponentially expanding said output voltage of said first load diode, thereby producing an output of said OTA; said output circuit being capable Of tuning its transconductance characteristic.
2. 2. The amplifier as claimed in claim 1, wherein said output circuit includes emitter-coupled first, second, and third bipolar transistors driven by a common tail current; said output voltage of said first load diode being applied across bases of said first and second transistors; said output of said OTA being derived from collectors of said first and second transistors; and a control voltage being applied to a base of said third transistor for tuning a transconductance of said output circuit.
3. 3. The amplifier as claimed in claim 2, wherein said first and second transistors of said output circuit have a same emitter area and said third transistor of said circuit has an emitter area K times as large as that of said first and second transistors, where K is a constant greater than unity.
4. 4. The amplifier as claimed in claim 1, wherein said output circuit includes emitter-coupled first, second, third, and fourth bipolar transistors driven by a common tail current; said output voltage of said first load diode being applied across bases of said first and second transistors; said output of the OTA being derived from collectors of said first and second transistors; and a control or tuning voltage being commonly applied to bases of said third and fourth transistors for tuning a transconductance of said output circuit.
5. 5. The amplifier as claimed in claim 4, wherein said first and second transistors of said output circuit have a same emitter area and said third and fourth transistors of said output circuit have a same emitter area (K/2) times as large as that of said first and second transistors, where K is a constant greater than unity.
6. 6. The amplifier as claimed in claim 1, wherein said output circuit includes a first unbalanced differential pair of emitter-coupled first and second bipolar transistors driven by a first common tail current and a second unbalanced differential pair of emitter-coupled third and fourth bipolar transistors driven by a second common tail current; said second transistor having an emitter area K times as large as that of said first transistor, where K is a constant greater than unity; said third transistor having an emitter area K times as large as that of said fourth transistor; bases of said first and third transistors being coupled together, and bases of said second and fourth transistors being coupled together; collectors of said first and third transistors being coupled together and collectors of said second and fourth transistors being coupled together; said output voltage of said first load diode being applied across said coupled bases of said first and third transistors and said coupled bases of said second and fourth transistors; and said output of said OTA being derived from said coupled collectors of said first and third transistors and said coupled collectors of said second and fourth transistors.
7. 7. The amplifier as claimed in claim 1, wherein said output the V-I converter has a completely-linear transconductance characteristic within a specific range of said differential input voltage.
8. 8. The amplifier as claimed in claim 1, further comprising a second load diode cascode-connected to said first load diode.
9. 9. The amplifier as claimed in claim 2, wherein K is equal to 2.
10. 10. An operational transconductance amplifier comprising: (a) a V-I converter for receiving a differential input voltage and for producing a pair of differential output currents according to said received input voltage; (b) a first pair of load diodes for converting logarithmically said pair of differential output currents of said V-I converter to first and second output voltages, respectively; and (c) an output circuit for exponentially expanding a difference between said first and second output voltages produced by said firstpair of load diodes, therebyproducinga differential output current of said OTA; said output circuit being capable of tuning its trans conductance characteristic.
11. 11. The amplifier as claimed in claim 10, wherein said output circuit is formed by a triple-tail cell including emitter-coupled first, second, and third bipolar transistors driven by a common tail current; a difference between said first and second output voltages of said first pair of load diodes being applied across bases of said first and second transistors; said differential output current of said OTA being derived from collectors of said first and second transistors; and a control voltage being applied to a base of said third transistor for tuning said trans conductance of said triple-tail cell.
12. 12. The amplifier as claimed in claim 11, wherein said first and second transistors of said triple-tail cell have a same emitter area and said third transistor of said triple-tail cell has an emitter area K times as large as that of said first and second transistors, where K is a constant greater than unity.
13. 13. The amplifier as claimed in claim 10, wherein said output circuit is formed by a quadritail cell including emitter-coupled first, second, third, and fourth bipolar transistors driven by a common tail current; said first and second output voltages of said first pair of load diodes being applied across bases of said first and second transistors; said differential output current of the OTA being derived from collectors of said first and second transistors; and a control voltage being commonly applied to bases of said third and fourth transistors for tuning said trans conductance of said quadritail cell.
14. 14. The amplifier as claimed in claim 13, wherein said first and second transistors of said quadritail cell have a same emitter area and said third and fourth transistors of said quadritail cell have a same emitter area (K/2) times as large as that of said first and second transistors, where K is a constant greater than unity.
15. 15. The amplifiera's cIaixtd in claim 10, wherein said output circuit includes a first unbalanced differential pair of emitter-coupled first and second bipolar transistors driven by a first common tail current and a second unbalanced differential pair of emitter-coupled third and fourth bipolar transistors driven by a second common tail current; said second transistor having an emitter area K times as large as that of said first transistor, where K is a constant greater than unity; said third transistor having an emitter area K times as large as that of said fourth transistor; bases of said first and third transistors being coupled together, and bases of said second and fourth transistors being coupled together; collectors of said first and third transistors being coupled together and collectors of said second and fourth transistors being coupled together, said output voltageofsaidfirstloaddiodebeingapplied across said coupled bases of said first and third transistors and said coupled bases of said second and fourth transistors; and said output of said OTA being derived from said coupled collectors of said first and third transistors and said coupled collectors of said second and fourth transistors.
16. 16. The amplifier as claimed in claim lO, wherein said output the V-I converter has a completely-linear transconductance characteristic within a specific range of said differential input voltage.
17. 17. The amplifier as claimed in claim 10, further comprising a second pair of load diodes cascode-connected to said first pair of load diodes, respectively.
18. 18. The amplifier as claimed in claim 11, wherein K is equal to 2.
19. 19. An operational transconductance amplifier substantially as herein described with reference to and as shown in any of Figures 3, 4, 6, 8, 10, 11 and 12 of the accompanying drawings.