AN6077: An IC Operational Transconductance Amplifier (OTA ...

An IC Operational Transconductance Amplifier
(OTA) With Power Capability
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October 2000 AN6077.3

[ /Title In 1969, the first triple operational transconductance 7 V+
(AN60 amplifier or OTA was introduced. The wide acceptance of
77) this new circuit concept prompted the development of the YZ
/Sub- single, highly linear operational transconductance amplifier,
ject the CA3080. Because of its extremely linear INVERTING 2 Q1 Q2 3 NON-INVERTING OUTPUT
(An IC transconductance characteristics with respect to amplifier INPUT INPUT 6
Opera- bias current, the CA3080 gained wide acceptance as a gain
tional control block. The CA3094 improved on the performance of AMPLIFIER W X
Transc the CA3080 through the addition of a pair of transistors; BIAS 5
onduc- these transistors extended the current carrying capability to
tance 300mA, peak. This new device, the CA3094, is useful in an CURRENT IABC
Ampli- extremely broad range of circuits in consumer and industrial
fier applications; this paper describes only a few of the many 4 V-
(OTA) consumer applications.
With FIGURE 2. CURRENT MIRRORS W, X, Y AND Z USED IN
Power What Is an OTA? THE OTA
Capa-
bility) The OTA, operational transconductance amplifier, concept is NORMALIZED OUTPUT CURRENT AND 1.0 DIFFERENTIAL AMPLIFIER
/Autho as basic as the transistor; once understood, it will broaden the DEVIATION FROM STRAIGHT LINE 0.8 TRANSFER CHARACTERISTIC
r () designer's horizons to new boundaries and make realizable 0.6
/Key- designs that were previously unobtainable. Figure 1 shows an 0.4 -100 -50 0 50 100 150
words equivalent diagram of the OTA. The differential input circuit is 0.2
(Inter- the same as that found on many modern operational
sil amplifiers. The remainder of the OTA is composed of current 0
Corpo- mirrors as shown in Figure 2. The geometry of these mirrors is -0.2
ration, such that the current gain is unity. Thus, by highly -0.4
power degenerating the current mirrors, the output current is -0.6
switch, precisely defined by the differential input amplifier. Figure 3 -0.8
power shows the output current transfer characteristic of the -1.0
ampli- amplifier. The shape of this characteristic remains constant
fier, and is independent of supply voltage. Only the maximum -150
pro- current is modified by the bias current.
gram- ΔVbe (mV)
mable
power 7 V+ FIGURE 3. THE OUTPUT CURRENT TRANSFER
switch) CHARACTERISTIC OF THE OTA IS THE SAME
/Cre- AS THAT OF AN IDEALIZED DIFFERENTIAL
ator () AMPLIFIER

2- OTA The major controlling factor in the OTA is the input amplifier
bias current IABC; as explained in Figure 1, the total output
RIN 6 IOUT = gm (±ein) current and gm are controlled by this current. In addition, the
input bias current, input resistance, total supply current, and
ein 2RO output resistance are all proportional to this amplifier bias
gm ein current. These factors provide the key to the performance of
this most flexible device, an idealized differential amplifier,
2RO i.e., a circuit in which differential input to single ended output
conversion can be realized. With this knowledge of the
3+ basics of the OTA, it is possible to explore some of the
applications of the device.
gm = 19.2 • IABC ±IOUT ≈ IABC
Max (mA)
(mS) (mA)
(mA)
4 V- RO ≈ 7.5/IABC
5 IABC (MΩ) (mA)

FIGURE 1. EQUIVALENT DIAGRAM OF THE OTA DC Gain Control

The methods of providing DC gain control functions are
numerous. Each has its advantage: simplicity, low cost, high
level control, low distortion. Many manufacturers who have
nothing better to offer propose the use of a four quadrant

1 1-888-INTERSIL or 1-888-468-3774 | Copyright © Intersil Corporation 2000

Application Note 6077

multiplier. This is analogous to using an elephant to carry a the improvement in linearity of the transfer characteristic.
twig. It may be elegant but it takes a lot to keep it going! Reduced input impedance does result from this shunt
When operated in the gain control mode, one input of the connection. Similar techniques could be used on the OTA
standard transconductance multiplier is offset so that only output, but then the output signal would be reduced and the
one half of the differential input is used; thus, one half of the correction circuitry further removed from the source of non
multiplier is being thrown away. linearity. It must be emphasized that the input circuitry is
differential.
The OTA, while providing excellent linear amplifier
characteristics, does provide a simple means of gain control. 7
For this application the OTA may be considered the
realization of the ideal differential amplifier in which the full DIODE CURRENT = 0mA
differential amplifier gm is converted to a single ended 6
output. Because the differential amplifier is ideal, its gm is
directly proportional to the operating current of the THD (PERCENT) 5 100
differential amplifier; in the OTA the maximum output current
is equal to the amplifier bias current IABC. Thus, by varying 4 IABC 80 S/N RATIO (dB)
the amplifier bias current, the amplifier gain may be varied:
A = gm RL where RL is the output load resistance. Figure 4 500μA CA3080A
shows the basic configuration of the OTA DC gain control
circuit. S/N RATIO

3 60

10μA 40
2

VX +6V IO = gm VX 1 THD 20
10 100
SIGNAL 0 0
INPUT 0.1 1.0 1.0V

7 AMPLITUDE INPUT VOLTAGE (mV)
MODULATED
51 2- FIGURE 5A.
IO OUTPUT
OTA 7
DIODE CURRENT = 0.5mA
CA3080A 6
6
51 3 + 10K

5 4 5 100
IABC -6V IABC

VM RM THD (PERCENT) 4 500μA CA3080A 80 S/N RATIO (dB)
S/N RATIO
GAIN
CONTROL 3 60
10μA

2 40

FIGURE 4. BASIC CONFIGURATION OF THE OTA DC GAIN 1 THD 20
CONTROL CIRCUIT
0 100 1V 0
As long as the differential input signal to the OTA remains 1 10 10V
under 50mV peak-to-peak, the deviation from a linear
transfer will remain under 5 percent. Of course, the total INPUT VOLTAGE (mV)
harmonic distortion will be considerably less than this value.
Signal excursions beyond this point only result in an FIGURE 5B.
undesired “compressed” output. The reason for this
compression can be seen in the transfer characteristic of the 7
differential amplifier in Figure 3. Also shown in Figure 3 is a DIODE CURRENT = 1mA
curve depicting the departure from a linear line of this
transfer characteristic. 6

The actual performance of the circuit shown in Figure 4 is 5 100
plotted in Figure 5. Both signal to noise ratio and total
harmonic distortion are shown as a function of signal input. THD (PERCENT) 4 500μA 80 S/N RATIO (dB)
Figures 5B and 5C show how the signal handling capability of 10μA 60
the circuit is extended through the connection of diodes on 3 40
the input as shown in Figure 6 [2]. Figure 7 shows total 20
system gain as a function of amplifier bias current for several 2 IABC
values of diode current. Figure 8 shows an oscilloscope CA3080A
reproduction of the CA3080 transfer characteristic as applied S/N THD
to the circuit of Figure 4. The oscilloscope reproduction of 1 RATIO
Figure 9 was obtained with the circuit shown in Figure 6. Note
0 0
DISTORTION IS PRIMARILY 10V
A FUNCTION OF SIGNAL INPUT

1 10 100 1V

INPUT VOLTAGE (mV)

FIGURE 5C.

FIGURE 5. PERFORMANCE CURVES FOR THE CIRCUIT OF
FIGURES 4 AND 6

2

Application Note 6077

EIN 2K 12 EO 100 0mA
51 2
4 3 CA3080A 6 10μA
2K 100μA DIODE
53 10K 10 CURRENT
0.5mA
86 + GAIN 1mA
7 14 DIODE
11 1.0
CURRENT

9 12 13 0.1

V-

Transistors from CA3046 array. 0.01 100 200 300 400 500
AGC System with extended input range. 0 IABC (μA)

FIGURE 6. A CIRCUIT SHOWING HOW THE SIGNAL FIGURE 7. TOTAL SYSTEM GAIN vs AMPLIFIER BIAS
HANDLING CAPABILITY OF THE CIRCUIT OF CURRENT FOR SEVERAL VALUES OF DIODE
FIGURE 4 CAN BE EXTENDED THROUGH THE CURRENT
CONNECTION OF DIODES ON THE INPUT

Horizontal: 25mV/Div. Vertical: 50μA/Div., IABC = 100μA Horizontal: 0.5V/Div. Vertical: 50μA/Div., IABC = 100μA,
Diode Current = 1mA
FIGURE 8. CA3080 TRANSFER CHARACTERISTIC FOR THE
CIRCUIT OF FIGURE 4 FIGURE 9. CA3080 TRANSFER CHARACTERISTIC FOR THE
CIRCUIT OF FIGURE 6
Simplified Differential Input to Single Ended
Output Conversion common mode range is that of the CA3080 differential
One of the more exacting configurations for operational
amplifiers is the differential to single-ended conversion amplifier. In addition, the gain characteristic follows the
circuit. Figure 10 shows some of the basic circuits that are
usually employed. The ratios of the resistors must be standard differential amplifier gm temperature coefficient of
precisely matched to assure the desired common mode -0.3%/oC. Although the system of Figure 11 does not
rejection. Figure 11 shows another system using the
CA3080 to obtain this conversion without the use of provide the precise gain control obtained with the standard
precision resistors. Differential input signals must be kept
under 126mV for better than 5 percent nonlinearity. The operational amplifier approach, it does provide a good

simple compromise suitable for many differential transducer

amplifier applications.

3

Application Note 6077

R2 The CA3094

DIFFERENTIAL R1 OUTPUT The CA3094 offers a unique combination of characteristics
INPUT +- that suit it ideally for use as a programmable gain block for
audio power amplifiers. It is a transconductance amplifier in
R3 R4 R1 = R3 which gain and open-loop bandwidth can be controlled
R2 R4 between wide limits. The device has a large reserve of
output-current capability, and breakdown and power
DIFFERENTIAL R4 R5 OUTPUT dissipation ratings sufficiently high to allow it to drive a
INPUT +- complementary pair of transistors. For example, a 12W
power amplifier stage (8Ω load) can be driven with peak
R1 currents of 35mA (assuming a minimum output transistor
beta of 50) and supply voltages of ±18V. In this application,
R2 +- the CA3094A is operated substantially below its supply
voltage rating of 44V max. and its dissipation rating of 1.6W
R3 R1 = R3 max. Also in this application, a high value of open-loop gain
suggests the possibility of precise adjustment of frequency
+- R4 = R6 response characteristics by adjustment of impedances in the
R5 R7 feedback networks.
R6 R7
Implicit Tone Controls
+-
In addition to low distortion, the large amount of loop gain
R1 and flexibility of feedback arrangements available when
using the CA3094 make it possible to incorporate the tone
DIFFERENTIAL R2 R3 controls into the feedback network that surrounds the entire
INPUT amplifier system. Consider the gain requirements of a
R1 = R4 phonograph playback system that uses a typical high quality
R2 R3 magnetic cartridge[3]. A desirable system gain would result
in from 2W to 5W of output at a recorded velocity of 1cm/s.
+- R4 Magnetic pickups have outputs typically ranging from 4mV to
OUTPUT 10mV at 5cm/s. To get the desired output, the total system
needs about 72dB of voltage gain at the reference
FIGURE 10. SOME TYPICAL DIFFERENTIAL TO SINGLE frequency.
ENDED CONVERSION CIRCUITS
Figure 12 is a block diagram of a system that uses a passive or
IABC +V “losser” type of tone control circuit that is inserted ahead of the
gain control. Figure 13 shows a system in which the tone
500μA controls are implicit in the feedback circuits of the power
5 amplifier. Both systems assume the same noise input voltage
at the equalizer and main-amplifier inputs. The feedback
2K 7 system shows a small improvement (3.8dB) in signal-to-noise
3 + ratio at maximum gain but a dramatic improvement (20dB) at
the zero gain position. For purposes of comparison, the
DIFFERENTIAL 2K CA3080 6 OUTPUT assumption is made that the tone controls are set “flat” in both
INPUT 2 cases.
- RL
4 10K Cost Advantages

V- In addition to the savings resulting from reduced parts count
and circuit size, the use of the CA3094 leads to further
A = gm RL at 500μA, IABC: savings in the power supply system. Typical values of power
supply rejection and common-mode rejection are 90dB and
gm ≈ 10mS. 100dB, respectively. An amplifier with 40dB of gain and 90dB
of power supply rejection would require 316mV of power
∴ A = 10mS x 10K = 100. supply ripple to produce 1mV of hum at the output. Thus, no
further filtering is required other than that given by the energy
FIGURE 11. A DIFFERENTIAL TO SINGLE ENDED storage capacitor at the output of the rectifier system.
CONVERSION CIRCUIT WITHOUT PRECISION
RESISTORS

4

Application Note 6077

ESIG = 40mV ESIG = 4mV ESIG = 4mV ATOTAL = 60dB EO = 4V

EQUALIZER TONE VOLUME BUFFER STAGE POWER
CONTROLS CONTROLS EN AT INPUT = 5 x 10-6 AMP
EN AREF = 32dB 10-6 8Ω
AT INPUT = 1 x -20dB

PICKUP EN = 40 x 10-6 EN = 4 x 10-6 EN = 4 x 10-6 SPEAKER
ESIG =1mV TOTAL GAIN = 72dB 4 EN = 6.23 x 10-3
EO 6.23 x 10-3 = 640 AT MAX VOL
EN =

EN = 4mV AT MIN VOL

FIGURE 12. BLOCK DIAGRAM OF A SYSTEM USING A “LOSSER” TYPE TONE CONTROL CIRCUIT

ESIG = 40mV ESIG = 40mV EO = 4V
ATOTAL = 60dB

EQUALIZER VOLUME AMPLIFIER WITH FEED-
CONTROLS BACK TONE CONTROLS
EN AREF = 32dB 10-6
AT INPUT = 1 x EN = 5 x 10-6

PICKUP EN = 40 x 10-6 EN = 40 x 10-6 4 EN = 4.03 x 10-3
ESIG =1mV 4.03 x 10-3 = 990 AT MAX VOL

EO =
EN

EN = 0.5mV AT MIN VOL

FIGURE 13. A SYSTEM IN WHICH TONE CONTROLS ARE IMPLICIT IN THE FEEDBACK CIRCUIT OF THE POWER AMPLIFIER

Power Amplifier Using the CA3094 A bias arrangement that can be accomplished at lower cost
than those already described replaces the Vbe multiplier with a
A complete power amplifier using the CA3094 and three 1N5391 diode in series with an 8.2Ω resistor. This arrangement
additional transistors is shown schematically in Figure 14. does not provide the degree of bias stability of the Vbe
The amplifier is shown in a single-channel configuration, but multiplier, but is adequate for many applications.
power supply values are designed to support a minimum of
two channels. The output section comprises Q1 and Q2, Tone-Controls
complementary epitaxial units connected in the familiar
“bootstrap” arrangement. Capacitor C3 provides added base The tone controls, the essential elements of the feedback
drive for Q1 during positive excursions of the output. The system, are located in two sets of parallel paths. The bass
circuit can be operated from a single power supply as well as network includes R3, R4, R5, C4, and C5. C6 blocks the DC
from a split supply as shown in Figure 15. The changes from the feedback network so that the DC gain from input to the
required for 14.4V operation with a 3.2Ω speaker are also feedback takeoff point is unity. The residual DC output voltage
indicated in the diagram. at the speaker terminals is then

The amplifier may also be modified to accept input from ⎝⎛⎜R1 -R----1---1-R---+--1--2-R-----1---2-⎞⎟⎠ IABC
ceramic phonograph cartridges. For standard inputs
(equalizer preamplifiers, tuners, etc.) C1 is 0.047μF, R1 is where R1 is the source resistance. The input bias current is
250kΩ, and R2 and C2 are omitted. For ceramic-cartridge then
inputs, C1 is 0.0047μF, R1 is 2.5MΩ, and the jumper across
C2 is removed. I--A--2--B--β--C-- = –-(--V----C---2-C---β---–-R---V--6--B----E-----)

Output Biasing The treble network consists of R7, R8, R9, R10, C7, C8, C9,
and C10. Resistors R7 and R9 limit the maximum available cut
Instead of the usual two-diode arrangement for establishing and boost, respectively. The boost limit is useful in curtailing
idling currents in Q1 and Q2, a “Vbe Multiplier”, transistor Q3, is heating due to finite turn-off time in the output units. The limit is
used. This method of biasing establishes the voltage between also desirable when there are tape recorders nearby. The cut
the base of Q1 and the base of Q2 at a constant multiple of the limit aids the stability of the amplifier by cutting the loop gain at
base to emitter voltage of a single transistor while maintaining a higher frequencies where phase shifts become significant.
low variational impedance between its collector and emitter
(see Appendix A). If transistor Q3 is mounted in intimate In cases in which absolute stability under all load conditions is
thermal contact with the output units, the operating temperature required, it may be necessary to insert a small inductor in the
of the heat sink forces the Vbe of Q3 up and down inversely output lead to isolate the circuit from capacitive loads. A 3μH
with heat-sink temperature. The voltage bias between the inductor (1A) in parallel with a 22Ω resistor is adequate. The
bases of Q1 and Q2 varies inversely with heat sink temperature derivation of circuit constants is shown in Appendix B. Curves
and tends to keep the idling current in Q1 and Q2 constant. of control action versus electrical rotation are also given.

5

Application Note 6077

“BOOST” R20 “CUT” C7 R7 + T1 120V AC TO
C10 (CW) 15K (CCW) 0.01μF 820Ω 26.8VCT AT 1A
- 4700μF
0.12μF R8 TREBLE D1
1800Ω C8 220Ω C3 D2 120V AC
1W 15μF D3
R9 0.001μF 5600Ω + D4
68Ω C9 220Ω
- 5μF+ 1W R2
0.001μF 1.8MΩ

Q1 - 4700
2N6292 μF
+
30Ω R11
C1 7 3pF 27Ω Q3 0.47Ω 330Ω
ES 1 2N6292 0.47Ω R12
2- 47Ω
R1

CA3094 8 Q2
2N6107

3+ 6

5 4
R6 1Ω
680K
0.47
μF

C6 C5 C4 C2
25μF 0.2μF BASS 0.02μF 0.47μF
R5 JUMPER
+- 1K

“BOOST” R4 “CUT” R3
(CW) 100K (CCW) 10K

FIGURE 14. A COMPLETE POWER AMPLIFIER USING THE CA3094 AND THREE ADDITIONAL TRANSISTORS

+36V
VCC

220K 0.12μF TREBLE R5 5.6K R1 -
5% 15K 1.2M 5μF 220Ω
0.01μF 1W +

68 R2 15μF
1.8K 220Ω
-
+ 820 1W Q1
0.001μF R3 2N6292
- 30Ω 0.47Ω
+ 1500μF
0.22μF 5 Q3 +-
27
100K R4 2N6292 330
CA3094 27Ω Ω
220K
5% 220K 8 0.47Ω

25μF 36 Q2 47Ω
1/2VCC 1 2N6107

4 1Ω 0.47μF

25μF 0.2μF 0.02μF 3pF
1/2VCC 1K

-+

100K 10K 47K
BASS

FIGURE 15. A POWER AMPLIFIER OPERATED FROM A SINGLE SUPPLY

6

Application Note 6077

Performance 2.0INTERMODULATION DISTORTION (%)
1.8
Figure 16 is a plot of the measured response of the complete
amplifier at the extremes of tone control rotation. A 1.6
comparison of Figure 16 with the computed curves of Figure
B4 (Appendix B) shows good agreement. The total harmonic 1.4
distortion of the amplifier with an unregulated power supply is
shown in Figure 17; IM distortion is plotted in Figure 18. Hum 1.2
and noise are typically 700μV at the output, or 83dB down.
1.0 60Hz 2kHz
60 BASS BOOST TREBLE BOOST 0.8 60Hz 7kHz
55
50 FLAT 0.6 60Hz 12kHz
45
EO/ES (dB) 40 0.4
35
30 TREBLE CUT 0.2
25
20 BASS CUT 0 2 4 6 8 10 12 14
15
10 3 6 8 2 3 68 2 3 6 8 2 3 68 OUTPUT POWER (W)
100 1000 10K 100K
2 FIGURE 18. IM DISTORTION OF THE AMPLIFIER WITH AN
10 FREQUENCY (Hz) UNREGULATED SUPPLY

FIGURE 16. THE MEASURED RESPONSE OF THE AMPLIFIER Companion RlAA Preamplifier
AT EXTREMES OF TONE CONTROL ROTATION
Many available preamplifiers are capable of providing the
TOTAL HARMONIC DISTORTION (%) 1.0 4kHz 16kHz 26kHz drive for the power amplifier of Figure 14. Yet the unique
1kHz characteristics of the amplifier, its power supply, input
impedance, and gain make possible the design of an RIAA
0.9 preamplifier that can exploit these qualities. Since the input
2kHz impedance of the amplifier is essentially equal to the value of
the volume control resistance (250kΩ), the preamplifier need
0.8 not have high output current capability. Because the gain of
the power amplifier is high (40dB) the preamplifier gain only
0.7 has to be approximately 30dB at the reference frequency
(1kHz) to provide optimum system gain.
0.6
Figure 19 shows the schematic diagram of a CA3080
0.5 preamplifier. The CA3080, a low cost OTA, provides
sufficient open-loop gain for all the bass boost necessary in
0.4 RIAA compensation. For example, a gm of 10mS with a load
resistance of 250kΩ provides an open-loop gain of 68dB,
0.3 26kHz thus allowing at least 18dB of loop gain at the lowest
frequency. The CA3080 can be operated from the same
0.2 1kHz 16kHz power supply as the main amplifier with only minimal
decoupling because of the high power supply rejection
0.1 inherent in the device circuitry. In addition, the high voltage
4kHz swing capability at the output enables the CA3080
preamplifier to handle badly over modulated (over-cut)
02 4 6 8 10 12 recordings without overloading. The accuracy of equalization
OUTPUT POWER (W) is within ±1dB of the RIAA curve, and distortion is virtually
immeasurable by classical methods. Overload occurs at an
FIGURE 17. TOTAL HARMONIC DISTORTION OF THE output of 7.5V, which allows for undistorted inputs of up to
AMPLIFIER WITH AN UNREGULATED POWER 186mV (260mV peak).
SUPPLY

7

Application Note 6077

120K V+ The derivative of Equation A1 with respect to I yields the
0.002μF 680pF 5.6K incremental impedance of the Vbe multiplier:

d---d-E---I--1- = Z = -β--R--+---1--1-- + 1 + -(--β----B-+----R-1---)1---R----2-- R-----2-K--I--e3----R-+---2--K----3- (EQ. A3)

3.9K 1.5M - 7 + EOUT where K3 is a constant of the transistor Q1 and can be found
5μF 2 CA3080 4 from:
3 + - 50μF
1μF
6

ES 56K Vbe = K3lnIe – K2 (EQ. A4)

5

56K 5.6K Equation A4 is but another form of the diode equation:

V- Ie = ISe -q---KV----T-b---e-- – 1 (EQ. A5)

120K

0.002μF 680pF Using the values shown in Figure 14, plus data on the
2N6292 (a typical transistor that could be used in the circuit),
+ 3.9K 1.5M - 7 6 EOUT the dynamic impedance of the circuit at a total current of
ES 2 CA3080 4 40mA is found to be 4.6Ω. In the actual design of the Vbe
5μF + - 50μF multiplier, the value of IR2 must be greater than Vbe or the
1μF 3 transistor will never become forward biased.
56K 5 +
Appendix B - Tone Controls
56K
Figure B1 shows four operational amplifier circuit
FIGURE 19. A CA3080 PREAMPLIFIER configurations and the gain expressions for each. The
asymptotic low frequency gain is obtained by letting S
approach zero in each case:

Appendix A - Vbe Multiplier Bass Boost: ALOW = R-----1----+-----RR-----22----+-----R-----3-
Bass Cut: ALOW = -R----1--R---+--2--R--+---2--R--+---3--R-----3-
The equivalent circuit for the Vbe multiplier is shown in
Figure A1. The voltage E1 is given by: Treble Boost: ALOW = -C----1--C---+--4--C-----4-

E1 = β--R---+--1---I1-- + Vbe 1 + R-----2---(--R-β---1--+-----1---)- (EQ. A1)

E1 Treble Cut: ALOW = C-----1--C---+--4--C-----4-

R1 The asymptotic high-frequency gain is obtained by letting S
I Vbe increase without limit in each expression:

R2 Ie Bass Boost: AHIGH = -R----1--R--+---2--R-----2-
Bass Cut: AHIGH = R-----1--R---+--2--R-----2-

FIGURE A1. EQUIVALENT CIRCUIT FOR THE Vbe MULTIPLIER Treble Boost : AHIGH = 1 + C1 ⎛ -C---C-3---3--+-C---C--4---4-⎠⎞⎟
⎜
The value of Vbe is itself dependent on the emitter current of ⎝
the transistor, which is, in turn, dependent on the input
current I since: Treble Cut: AHIGH = -C----2---C--+--1---C-----+C----1----C--1---+---C--2----C----4------4--

Ie = I – -V-R---b--2-e- (EQ. A2)

8

Application Note 6077

Note that the expressions for high frequency gain are :
identical for both bass circuits, while the expressions for low
frequency gain are identical for the treble circuits. Bass Circuit: ALOW(Boost) = 10AMID
ALOW(Cut) = -A----1M---0--I-D---
Figure B2 shows cut and boost bass and treble controls that
have the characteristics of the circuits of Figure B1. The Treble Circuit: AHIGH(Boost) = 10AMID
value REFF in the treble controls of Figure B1 is derived from AHIGH(Cut) = -A----1M---0--I-D---
the parallel combination of R1 and R2 of Figure B2 when the
control is rotated to its maximum counterclockwise position. then the following relationships result:
When the control is rotated to its maximum clockwise
position, the value is equal to R1. Bass Circuit: R1 = 10R2
R3 = 99R2
To compute the circuit constants, it is necessary to decide in
advance the amounts of boost and cut desired. The gain Treble Circuit: C1 = 10C4
expressions of Figure B1 indicate that the slope of the C2 = -1---09----C9----4--
amplitude versus frequency curve in each case will be 6dB
per octave (20dB per decade). If the ratios of boosted and
cut gain are set at 10, i.e.

R2 C1 C2 R1 EO
ES R3 R1 R2 R3
+-
+- EO ES

A = ⎛ -R----1----+-----RR-----22----+-----R-----3-⎠⎟⎞ -1----+-----S-----C---1-1----(-+--(--R--R---S-----2--1--R--R----+---3--3-----RC----+-----12-----R----+-----1-----R--R-------3--3-----)--) A = ⎛ R-----1--R--+---2--R--+---2--R--+---3--R-----3-⎠⎟⎞ -1----+-----S-----C----2----(---(--R--R--------2--1----R----+-----3-----R----+-----2-----R----+-----1-----R--R-------3--3-----)--)
⎜ ⎜
⎝ ⎝ ⎛ -R--R--2---2--+-R---R--3---3-⎟⎞⎠
⎜
1 + S C2 ⎝

ALOW FREQUENCY = -R----1-----+----RR-----22----+-----R-----3- ALOW FREQUENCY = R-----1--R---+--2--R--+---2--R--+---3--R-----3-

FIGURE B1 (A). BASS BOOST FIGURE B1 (B). BASS CUT

C1 C3 EO C2 C4 EO
ES C4 C1 REFF
+-
+- REFF ES

A = ⎛ -C----1--C--+---4--C-----4-⎠⎞⎟ -1----+-----S-----R----E----F----F--1---(----C--+-------1--S-----C----R-----4----E---(--+--F--C------CF--1------C3----+----C3------C--4------4----+----)------C--------1-------C---------3--------) A = ⎛ -C----1--C---+--4--C-----4-⎞⎟⎠ 1-----+-----S-----R----E1----F-+---F--S---(----C--R--------1E------C--F-------4-F------((--+----CC------C--11------2----++----C------CC--4------24----+----))------C--------1--------C--------2--------)
⎜ ⎜
⎝ ⎝

ALOW FREQUENCY = -C----1--C--+---4--C-----4- ALOW FREQUENCY = -C----1--C---+--4--C-----4-

FIGURE B1 (C). TREBLE BOOST FIGURE B1 (D). TREBLE CUT

FIGURE B1. FOUR OPERATIONAL AMPLIFIER CIRCUIT CONFIGURATIONS AND THE GAIN EXPRESSIONS FOR EACH

9

Application Note 6077

The unaffected portion of the gain (AHIGH for the bass R2 CW R3 CCW R1
control and ALOW for the treble control) is 11 in each case.
C2
To make the controls work symmetrically, the low and high C1
frequency break points must be equal for both boost and cut.
-
Thus:
+
Bass Control:-C---R-1---R-1----+3---(--R-R---2-1----+-+----R-R---3-2----) = C--R---2-2--R---+--2--R-R----3-3-
FIGURE B2 (A). BASS CONTROL
and C1R3 = -C---R-2---R-1----+3---(--R-R---2-1----+-+----R-R---3-2----)
C1 CW R1 CCW C4
since R3 ≅ R2 + R3, C2 = 10C1

Treble Control: R1 (---C-----1---C----4-----+--C---C-1---3--+--C---C-4---4--+-----C----1----C----3----)

= R---R--1---1--+-R---R--2---2- (C1 + C2) R2

and R2C3 = ⎛ -R--R--1---1--+-R---R--2---2-⎠⎟⎞ -(--C----1----C----4----(-+--C---C-1---2--+--C---C-4---4--+--)---C----1----C----2----) C3
⎜
⎝ C2 -

since C1 ≅ 100C2, C2 = C3 and C1 = 10C4, R1 = 9R2 +

To make the controls work in the circuit of Figure 14, breaks
were set at 1000Hz:

for the base control 0.1 C1 R 3 = 1 FIGURE B2 (B). TREBLE CONTROL
2----π-----×-----1---0----0---0--
FIGURE B2. CUT AND BOOST BASS AND TREBLE CONTROLS
and for the treble control R1C3 = 1 THAT HAVE THE CHARACTERISTICS OF THE
-2---π-----×-----1---0----0---0-- CIRCUITS IN FIGURE B1

Response and Control Rotation 68Ω 0.12μF 15K 0.01μF
820Ω
In a practical design, it is desirable to make “flat” response 1.8K P 0.001
correspond to the 50% rotation position of the control, and to μF
have an aural sensation of smooth variation of response on
either side of the mechanical center. It is easy to show that 0.001μF ES - EO
the “flat” position of the bass control occurs when the wiper 0.2 P = 1.0
arm is advanced to 91% of its total resistance. The +
amplitude response of the treble control is, however, never P = 0.99
completely “flat”; a computer was used to generate response 45 1K μF 0.02
curves as controls were varied. Q = 1.0 μF P=0
10K 100K
40 Q

Figure B3 is a plot of the response with bass and treble tone EO/ES (dB) 35 Q = 0.99 100K 10K
controls combined at various settings of both controls. The
values shown are the practical ones used in the actual Q = 0.98 P = 0.98
design. Figure B4 shows the information of Figure B3 30 P = 0.96
replotted as a function of electrical rotation. The ideal taper
for each control would be the complement of the 100Hz plot Q = 0.96
for the bass control and the 10kHz response for the treble 25
control. The mechanical center should occur at the
crossover point in each case. Q =0.914
20 Q = 0.85

15 Q=0 Q = 0.75 P = 0.92
10 100 Q = 0.5 P = 0.8
Q = 0.2 P = 0.5
5 P = 0.3
0 P = 0.1

10 P = 0.05

1000
FREQUENCY (Hz)

FIGURE B3. A PLOT OF THE RESPONSE OF THE CIRCUIT OF
FIGURE 14 WITH BASS AND TREBLE TONE
CONTROLS COMBINED AT VARIOUS SETTINGS
OF BOTH CONTROLS

10

Application Note 6077

45 40

40 35

35 30

30GAIN (dB) 25 1kHz
GAIN (dB)
25 20 31.6kHz
10kHz
20 1000Hz
15 100Hz 15
10 31.6Hz
10
5
5
0
0.2 0.4 0.6 0.8 1.0 0
0.2 0.4 0.6 0.8 1.0
ELECTRICAL ROTATION OF BASS CONTROL
ELECTRICAL ROTATION OF TREBLE CONTROL
FIGURE B4 (A).
FIGURE B4 (B).
References
FIGURE B4. THE INFORMATION OF FIGURE B3 PLOTTED AS
For Intersil documents available on the internet, see web site A FUNCTION OF ELECTRICAL ROTATION
http://www.intersil.com/

[1] AN6668 Application Note, “Applications of the CA3080
and CA3080A High Performance Operational
Transconductance Amplifiers,” H. A. Wittlinger, Intersil
Corporation.

[2] “A New Wide-Band Amplifier Technique,” B. Gilbert,
IEEE Journal of Solid State Circuits, Vol. SC-3, No. 4,
December, 1968.

[3] “Trackability,” James A. Kogar, Audio, December, 1966.

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