An IC Operational Transconductance Amplifier
(OTA) With Power Capability
Semiconductor
Application Note
In 1969, the first triple operational transconductance amplifier
or OTA was introduced. The wide acceptance of this new circuit concept prompted the development of the single, highly
linear operational transconductance amplifier, the CA3080.
Because of its extremely linear transconductance characteristics with respect to amplifier bias current, the CA3080 gained
wide acceptance as a gain control block. The CA3094
improved on the performance of the CA3080 through the
addition of a pair of transistors; these transistors extended the
current carrying capability to 300mA, peak. This new device,
the CA3094, is useful in an extremely broad range of circuits
in consumer and industrial applications; this paper describes
only a few of the many consumer applications.
What Is an OTA?
April 1994
7
Y
AMPLIFIER
BIAS
CURRENT
-
5
W
2RO
gm ein
6
IOUT = gm (±ein)
2RO
+
4 V5 IABC
NON-INVERTING
3
INPUT
6
X
IABC
4
V-
NORMALIZED OUTPUT CURRETN AND
DEVIATION FROM STRAIGHT LINE
1.0
DIFFERENTIAL AMPLIFIER
TRANSFER CHARACTERISTIC
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-100
-50
0
50
∆Vbe (mV)
100
150
FIGURE 3. THE OUTPUT CURRENT TRANSFER CHARACTERISTIC OF THE OTA IS THE SAME AS THAT OF AN
IDEALIZED DIFFERENTIAL AMPLIFIER
OTA
RIN
3
2
Q1 Q2
V+
ein
Z
OUTPUT
INVERTING
INPUT
-1.0
-150
2
V+
FIGURE 2. CURRENT MIRRORS W, X, Y AND Z USED IN THE OTA
The OTA, operational transconductance amplifier, concept is as
basic as the transistor; once understood, it will broaden the
designer's horizons to new boundaries and make realizable
designs that were previously unobtainable. Figure 1 shows an
equivalent diagram of the OTA. The differential input circuit is
the same as that found on many modern operational amplifiers.
The remainder of the OTA is composed of current mirrors as
shown in Figure 2. The geometry of these mirrors is such that
the current gain is unity. Thus, by highly degenerating the current mirrors, the output current is precisely defined by the differential input amplifier. Figure 3 shows the output current transfer
characteristic of the amplifier. The shape of this characteristic
remains constant and is independent of supply voltage. Only
the maximum current is modified by the bias current.
7
AN6077.1
gm = 19.2 • IABC
(mA)
(mS)
RO ≈ 7.5/IABC
(MΩ)
(mA)
±IOUT ≈ IABC
Max (mA)
(mA)
FIGURE 1. EQUIVALENT DIAGRAM OF THE OTA
The major controlling factor in the OTA is the input amplifier
bias current IABC; as explained in Figure 1, the total output
current and gm are controlled by this current. In addition, the
input bias current, input resistance, total supply current, and
output resistance are all proportional to this amplifier bias
current. These factors provide the key to the performance of
this most flexible device, an idealized differential amplifier,
i.e., a circuit in which differential input to single ended output
conversion can be realized. With this knowledge of the
basics of the OTA, it is possible to explore some of the applications of the device.
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
multiplier. This is analogous to using an elephant to carry a
twig. It may be elegant but it takes a lot to keep it going!
When operated in the gain control mode, one input of the
1
Copyright
© Harris Corporation 1998
Application Note 6077
standard transconductance multiplier is offset so that only
one half of the differential input is used; thus, one half of the
multiplier is being thrown away.
OTA
CA3080A
3
+
6
IO
10K
5
-6V
IABC
VM
RM
GAIN
CONTROL
3
60
10µA
2
40
1.0
2
0
1.0V
100
10
INPUT VOLTAGE (mV)
FIGURE 5A.
7
DIODE CURRENT = 0.5mA
6
FIGURE 4. BASIC CONFIGURATION OF THE OTA DC GAIN
CONTROL CIRCUIT
5
500µA
4
100
IABC
CA3080A 80
S/N RATIO
3
60
10µA
2
40
THD
20
0
0
1
10
10V
1V
100
INPUT VOLTAGE (mV)
FIGURE 5B.
7
DIODE CURRENT = 1mA
6
THD (PERCENT)
The actual performance of the circuit shown in Figure 4 is
plotted in Figure 5. Both signal to noise ratio and total harmonic distortion are shown as a function of signal input. Figures 5B and 5C show how the signal handling capability of
the circuit is extended through the connection of diodes on
the input as shown in Figure 6[2]. Figure 7 shows total system
gain as a function of amplifier bias current for several values
of diode current. Figure 8 shows an oscilloscope reproduction of the CA3080 transfer characteristic as applied to the
circuit of Figure 4. The oscilloscope reproduction of Figure 9
was obtained with the circuit shown in Figure 6. Note the
improvement in linearity of the transfer characteristic.
Reduced input impedance does result from this shunt connection. Similar techniques could be used on the OTA output,
but then the output signal would be reduced and the correction circuitry further removed from the source of non linearity.
It must be emphasized that the input circuitry is differential.
20
THD
1
As long as the differential input signal to the OTA remains
under 50mV peak-to-peak, the deviation from a linear transfer will remain under 5 percent. Of course, the total harmonic
distortion will be considerably less than this value. Signal
excursions beyond this point only result in an undesired
“compressed” output. The reason for this compression can
be seen in the transfer characteristic of the differential amplifier in Figure 3. Also shown in Figure 3 is a curve depicting
the departure from a linear line of this transfer characteristic.
80
S/N RATIO (dB)
500µA
0
0.1
IO = gm VX
AMPLITUDE
MODULATED
OUTPUT
4
4
S/N RATIO (dB)
51
2
100
IABC
CA3080A
S/N RATIO
5
100
4
80
500µA
3
60
IABC
CA3080A
S/N
1
RATIO
10µA
2
S/N RATIO (dB)
7
51
5
1
THD (PERCENT)
+6V
VX
SIGNAL
INPUT
DIODE CURRENT = 0mA
6
THD (PERCENT)
The OTA, while providing excellent linear amplifier characteristics, does provide a simple means of gain control. For this
application the OTA may be considered the realization of the
ideal differential amplifier in which the full differential amplifier gm is converted to a single ended output. Because the
differential amplifier is ideal, its gm is directly proportional to
the operating current of the differential amplifier; in the OTA
the maximum output current is equal to the amplifier bias
current IABC. Thus, by varying the amplifier bias current, the
amplifier gain may be varied: A = gm RL where RL is the output load resistance. Figure 4 shows the basic configuration
of the OTA DC gain control circuit.
7
40
THD
20
0
0
DISTORTION IS PRIMARILY
A FUNCTION OF SIGNAL INPUT
1
10
10V
100
INPUT VOLTAGE (mV)
10V
FIGURE 5C.
FIGURE 5. PERFORMANCE CURVES FOR THE CIRCUIT OF
FIGURES 4 AND 6
Application Note 6077
100
2K
51
2
2
3
2K
10K
6
10
6
3
5
100µA
EO
CA3080A
4
8
0mA
10µA
1
+
DIODE
CURRENT
0.5mA
1mA
GAIN
EIN
1.0
7
14
11
9 12
DIODE
CURRENT
0.1
13
V0.01
Transistors from CA3046 array
AGC System with extended input range
FIGURE 6. A CIRCUIT SHOWING HOW THE SIGNAL HANDLING CAPABILITY OF THE CIRCUIT OF
FIGURE 4 CAN BE EXTENDED THROUGH THE
CONNECTION OF DIODES ON THE INPUT
Horizontal: 25mV/Div. Vertical: 50µA/Div.
IABC = 100µA
FIGURE 8. OSCILLOSCOPE REPRODUCTION OF THE CA3080
TRANSFER CHARACTERISTIC AS APPLIED TO
THE CIRCUIT OF FIGURE 4
Simplified Differential Input to Single Ended Output
Conversion
One of the more exacting configurations for operational
amplifiers is the differential to single-ended conversion circuit. Figure 10 shows some of the basic circuits that are usually employed. The ratios of the resistors must be precisely
matched to assure the desired common mode rejection. Figure 11 shows another system using the CA3080 to obtain
this conversion without the use of precision resistors. Differential input signals must be kept under 126mV for better
than 5 percent nonlinearity. The common mode range is that
of the CA3080 differential amplifier. In addition, the gain
characteristic follows the standard differential amplifier gm temperature coefficient of -0.3%/oC. Although the system of
Figure 11 does not provide the precise gain control obtained
3
0
100
200
300
400
IABC (µA)
500
FIGURE 7. TOTAL SYSTEM GAIN AS A FUNCTION OF AMPLIFIER BIAS CURRENT FOR SEVERAL VALUES OF
DIODE CURRENT
Horizontal: 0.5V/Div. Vertical: 50µA/Div.
IABC = 100µA, Diode Current = 1mA
FIGURE 9. OSCILLOSCOPE REPRODUCTION OF THE CA3080
TRANSFER CHARACTERISTIC AS APPLIED TO
THE CIRCUIT OF FIGURE 6
with the standard operational amplifier approach, it does
provide a good simple compromise suitable for many differential transducer amplifier applications.
Application Note 6077
The CA3094
R2
R1
+
DIFFERENTIAL
INPUT
R3
R4
OUTPUT
R1
R3
=
R2
R4
R4
R5
+
R1
DIFFERENTIAL
INPUT
+
R2
OUTPUT
R1 = R3
R3
+
R4 R6
=
R5 R7
R6
R7
The CA3094 offers a unique combination of characteristics
that suit it ideally to use as a programmable gain block for
audio power amplifiers. It is a transconductance amplifier in
which gain and open-loop bandwidth can be controlled
between wide limits. The device has a large reserve of output-current capability, and breakdown and power dissipation
ratings sufficiently high to allow it to drive a complementary
pair of transistors. For example, a 12W power amplifier stage
(8Ω load) can be driven with peak currents of 35mA (assuming a minimum output transistor beta of 50) and supply voltages of ±18V. In this application, the CA3094A is operated
substantially below its supply voltage rating of 44V max. and
its dissipation rating of 1.6W max. Also in this application, a
high value of open-loop gain suggests the possibility of precise adjustment of frequency response characteristics by
adjustment of impedances in the feedback networks.
Implicit Tone Controls
+
R1
R3
DIFFERENTIAL
INPUT
R2
R1
R4
=
R2
R3
R4
+
OUTPUT
FIGURE 10. SOME TYPICAL DIFFERENTIAL TO SINGLEENDED CONVERSION CIRCUITS
+V
IABC
500µA
5
2K
7
3
+
2
-
4
OUTPUT
RL
10K
-V
NOTES:
1. A = gm RL
AT 500µA, IABC
2. gm ≈ 10mS
3. ∴
Figure 12 is a block diagram of a system that uses a passive or
“losser” type of tone control circuit that is inserted ahead of the
gain control. Figure 13 shows a system in which the tone controls are implicit in the feedback circuits of the power amplifier.
Both systems assume the same noise input voltage at the
equalizer and main-amplifier inputs. The feedback system
shows a small improvement (3.8dB) in signal-to-noise ratio at
maximum gain but a dramatic improvement (20dB) at the zero
gain position. For purposes of comparison, the assumption is
made that the tone controls are set “flat” in both cases.
Cost Advantages
6
CA3080
2K
In addition to low distortion, the large amount of loop gain and
flexibility of feedback arrangements available when using the
CA3094 make it possible to incorporate the tone controls into
the feedback network that surrounds the entire amplifier system. Consider the gain requirements of a phonograph playback system that uses a typical high quality magnetic
cartridge.[3] A desirable system gain would result in from 2W
to 5W of output at a recorded velocity of 1cm/s. Magnetic
pickups have outputs typically ranging from 4mV to 10mV at
5cm/s. To get the desired output, the total system needs
about 72dB of voltage gain at the reference frequency.
A = 10mS x 10K = 100
FIGURE 11. A DIFFERENTIAL TO SINGLE ENDED CONVERSION CIRCUIT WITHOUT PRECISION RESISTORS
4
In addition to the savings resulting from reduced parts count
and circuit size, the use of the CA3094 leads to further savings in the power supply system. Typical values of power supply rejection and common-mode rejection are 90dB and
100dB, respectively. An amplifier with 40dB of gain and 90dB
of power supply rejection would require 316mV of power supply ripple to produce 1mV of hum at the output. Thus, no further filtering is required other than that given by the energy
storage capacitor at the output of the rectifier system.
Application Note 6077
E SIG = 40mV
PICKUP
E SIG =1mV
E SIG = 4mV
E SIG = 4mV
EO = 4V
A TOTAL = 60dB
EQUALIZER
A REF = 32dB
EN AT INPUT = 1 x 10-6
TONE
CONTROLS
-20dB
EN = 40 x 10-6
VOLUME
CONTROLS
EN = 4 x 10-6
BUFFER STAGE
EN AT INPUT = 5 x 10-6
EN = 4 x 10-6
TOTAL GAIN = 72dB
EO
EN
POWER
AMP
8Ω
SPEAKER
EN = 6.23 x 10-6
4
=
6.23 x 10-3
= 640 AT MAX VOL
EN = 4mV AT MIN VOL
FIGURE 12. BLOCK DIAGRAM OF A SYSTEM USING A “LOSSER” TYPE TONE CONTROL CIRCUIT
E SIG = 40mV
EO = 4V
E SIG = 40mV
A TOTAL = 60dB
EQUALIZER
A REF = 32dB
EN AT INPUT = 1 x 10-6
VOLUME
CONTROLS
EN = 40 x 10-6
BUFFER STAGE
EN AT INPUT = 5 x 10-6
EN = 40 x 10-6
EO
EN
4
=
EN = 4.03 x 10-3
4.03 x 10-3
= 990 AT MAX VOL
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 complete power amplifier using the CA3094 and three additional transistors is shown schematically in Figure 14. The
amplifier is shown in a single-channel configuration, but power
supply values are designed to support a minimum of two channels. The output section comprises Q1 and Q2, complementary
epitaxial units connected in the familiar “bootstrap” arrangement. Capacitor C3 provides added base drive for Q1 during
positive excursions of the output. The circuit can be operated
from a single power supply as well as from a split supply as
shown in Figure 15. The changes required for 14.4V operation
with a 3.2Ω speaker are also indicated in the diagram.
The amplifier may also be modified to accept input from
ceramic phonograph cartridges. For standard inputs (equalizer
preamplifiers, tuners, etc.) C1 is 0.047µF, R1 is 250kΩ, and R2
and C2 are omitted. For ceramic-cartridge inputs, C1 is
0.0047µF, R1 is 2.5MΩ, and the jumper across C2 is removed.
Output Biasing
Instead of the usual two-diode arrangement for establishing
idling currents in Q1 and Q2, a “Vbe Multiplier”, transistor Q3, is
used. This method of biasing establishes the voltage between
the base of Q1 and the base of Q2 at a constant multiple of the
base to emitter voltage of a single transistor while maintaining a
low variational impedance between its collector and emitter
(see Appendix A). If transistor Q3 is mounted in intimate thermal contact with the output units, the operating temperature of
the heat sink forces the Vbe of Q3 up and down inversely with
heat-sink temperature. The voltage bias between the bases of
Q1 and Q2 varies inversely with heat sink temperature and
tends to keep the idling current in Q1 and Q2 constant.
A bias arrangement that can be accomplished at lower cost
5
than those already described replaces the Vbe multiplier with a
1N5391 diode in series with an 8.2Ω resistor. This arrangement
does not provide the degree of bias stability of the Vbe multiplier, but is adequate for many applications.
Tone-Controls
The tone controls, the essential elements of the feedback system, are located in two sets of parallel paths. The bass network
includes R3, R4, R5, C4, and C5. C6 blocks the dc from the
feedback network so that the DC gain from input to the feedback takeoff point is unity. The residual DC output voltage at the
speaker terminals is then
R11 + R12
R1 ----------------------------R12
where R1 is the source resistance. The input bias current is
then
I ABC
( V CC + V BE )
--------------- = ------------------------------------2β
2βR6
The treble network consists of R7, R8, R9, R10, C7, C8, C9,
and C10. Resistors R7 and R9 limit the maximum available cut
and boost, respectively. The boost limit is useful in curtailing
heating due to finite turn-off time in the output units. The limit is
also desirable when there are tape recorders nearby. The cut
limit aids the stability of the amplifier by cutting the loop gain at
higher frequencies where phase shifts become significant.
In cases in which absolute stability under all load conditions is
required, it may be necessary to insert a small inductor in the
output lead to isolate the circuit from capacitive loads. A 3µH
inductor (1A) in parallel with a 22Ω resistor is adequate. The
derivation of circuit constants is shown in Appendix B. Curves
of control action versus electrical rotation are also given.
Application Note 6077
C7
R7
“CUT”
(CCW) 0.01µF 820Ω
“BOOST” R20
(CW) 15K
0.12µF
R9
68Ω
T1
+
C9
C3
15µF
5600Ω
+
220Ω
1W
0.001µF
-
5µF
+
D3
Q1
2N6292
30Ω
7
C1
Q3
2N6292
1
+
2
D4
R11
330Ω
Q2
2N6107
8
-
4700
µF
0.47Ω
27Ω
CA3094
3
+
0.47Ω
3pF
ES
R1
120V AC
D2
220Ω
1W
0.001µF
D1
4700µF
-
R8
TREBLE
1800Ω
C8
120V AC TO
26.8VCT AT 1A
R12
47Ω
6
R2
1.8MΩ
4
5
1Ω
R6
680K
0.47
µF
C5
0.2µF
C6
25µF
-
BASS
“BOOST” R4
(CW) 100K
C4
0.02µF
“CUT”
(CCW)
C2
0.47µF
R3
10K
JUMPER
FIGURE 14. A COMPLETE POWER AMPLIFIER USING THE CA3094 AND THREE ADDITIONAL TRANSISTORS
+36V
VCC
220K
5%
0.12µF
R5
1.2M
TREBLE
15K
68
R1
220Ω
1W +
5.6K
0.01µF
+
1.8K
5µF
820
0.001µF
R3
30Ω
5
0.22µF
220K
+
220K
5%
6
3
4
0.02µF
100K
BASS
10K
Q1
2N6292
0.47Ω
Q3
2N6292
1500µF
+ 330
Ω
0.47Ω
Q2
2N6107
1
0.2µF
1K
8
CA3094
25µF
1/2VCC
25µF
1/2VCC
- +
R4
27Ω
7
2
100K
-
R2 15µF
220Ω
1W
-
+
R5
1K
1Ω
47Ω
0.47µF
3pF
47K
FIGURE 15. A POWER AMPLIFIER OPERATED FROM A SINGLE SUPPLY
6
Application Note 6077
Performance
Companion RlAA Preamplifier
Figure 16 is a plot of the measured response of the complete
amplifier at the extremes of tone control rotation. A comparison of Figure 16 with the computed curves of Figure B4
(Appendix B) shows good agreement. The total harmonic distortion of the amplifier with an unregulated power supply is
shown in Figure 17; IM distortion is plotted in Figure 18. Hum
and noise are typically 700µV at the output, or 83dB down.
Many available preamplifiers are capable of providing the
drive for the power amplifier of Figure 14. Yet the unique
characteristics of the amplifier, its power supply, input impedance, and gain make possible the design of an RIAA preamplifier that can exploit these qualities. Since the input
impedance of the amplifier is essentially equal to the value of
the volume control resistance (250kΩ), the preamplifier need
not have high output current capability. Because the gain of
the power amplifier is high (40dB) the preamplifier gain only
has to be approximately 30dB at the reference frequency
(1kHz) to provide optimum system gain.
60
TREBLE BOOST
BASS BOOST
55
50
45
FLAT
EOES (dB)
40
35
30
25
TREBLE CUT
20
BASS CUT
15
10
2
3 68
2
100
10
3 68
2
1000
3 68
2
10K
3 68
100K
FREQUENCY (Hz)
FIGURE 16. THE MEASURED RESPONSE OF THE AMPLIFIER
AT EXTREMES OF TONE CONTROL ROTATION
26kHz
1kHz
0.9
2kHz
0.8
120K
16kHz
0.7
+V
0.6
5.6K
0.002µF 680pF
4kHz
TOTAL HARMONIC DISTORTION (%)
1.0
Figure 19 shows the schematic diagram of a CA3080 preamplifier. The CA3080, a low cost OTA, provides sufficient openloop gain for all the bass boost necessary in AIAA compensation. For example, a gm of 10mS with a load resistance of
250kΩ provides an open-loop gain of 68dB, thus allowing at
least 18dB of loop gain at the lowest frequency. The CA3080
can be operated from the same power supply as the main
amplifier with only minimal decoupling because of the high
power supply rejection inherent in the device circuitry. In addition, the high voltage swing capability at the output enables
the CA3080 preamplifier to handle badly over modulated
(over-cut) recordings without overloading. The accuracy of
equalization is within ±1dB of the RIAA curve, and distortion
is virtually immeasurable by classical methods. Overload
occurs at an output of 7.5V, which allows for undistorted
inputs of up to 186mV (260mV peak).
0.5
1.5M
0.4
0.3
26kHz
0.2
2
5µF
16kHz
1kHz
3
4kHz
2
0
4
6
8
10
POWER OUTPUT (W)
12
ES
-
+
50µF
6
CA3080
1µF
0.1
+
7
3.9K
EOUT
-
4
56K
5
FIGURE 17. TOTAL HARMONIC DISTORTION OF THE AMPLIFIER WITH AN UNREGULATED POWER SUPPLY
56K
5.6K
INTERMODULATION DISTORTION (%)
-V
120K
2.0
1.8
0.002µF 680pF
1.6
1.4
1.5M
1.2
60Hz
2kHz
1.0
60Hz
7kHz
0.8
60Hz
12kHz
7
3.9K
5µF
2
+
3
-
0.4
ES
0.2
EOUT
4
56K
5
0
2
4
6
8
10
12
14
6
CA3080
1µF
0.6
56K
50µF
+
POWER OUTPUT (W)
FIGURE 18. IM DISTORTION OF THE AMPLIFIER WITH AN UNREGULATED SUPPLY
7
FIGURE 19. A CA3080 PREAMPLIFIER
Application Note 6077
Appendix A - Vbe Multiplier
The equivalent circuit for the Vbe multiplier is shown in Figure A1. The voltage E1 is given by:
R1I
R1
E1 = ------------- + V be 1 + ------------------------β+1
R2 ( β + 1 )
(A1)
+ R2 + R3
Bass Cut: A LOW = R1
------------------------------------R2 + R3
+ C4
Treble Boost : A LOW = C1
---------------------C4
+ C4
Treble Cut : A LOW = C1
---------------------C4
E1
The asymptotic high-frequency gain is obtained by letting S
increase without limit in each expression:
R1
I
+ R2 + R3
Bass Boost: A LOW = R1
------------------------------------R2
+ R2
Bass Boost: A HIGH = R1
---------------------R2
Vbe
R2
+ R2
Bass Cut: A HIGH = R1
---------------------R2
Ie
Treble Boost : A HIGH = 1 + C1  ----------------------
C3C4
C3 + C4
FIGURE A1. EQUIVALENT CIRCUIT FOR THE Vbe MULTIPLIER
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:
C1C4
C2 + ---------------------C1 + C4
Treble Cut: A HIGH = ------------------------------------C1 + C2
V be
I e = I – ---------R2
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.
(A2)
The derivative of Equation A1 with respect to I yields the
incremental impedance of the Vbe multiplier:
K3R2
dE1
R1
BR1
----------- = Z = ------------- + 1 + ------------------------- --------------------------dI
β+1
( β + 1 )R2 R2I e + K3
(A3)
where K3 is a constant of the transistor Q1 and can be found
from:
V be = K3 l n I e – K2
(A4)
Equation A4 is but another form of the diode equation:
Figure B2 shows cut and boost bass and treble controls that
have the characteristics of the circuits of Figure B1. The
value REFF in the treble controls of Figure B1 is derived from
the parallel combination of R1 and R2 of Figure B2 when the
control is rotated to its maximum counterclockwise position.
When the control is rotated to its maximum clockwise position, the value is equal to R1.
To compute the circuit constants, it is necessary to decide in
advance the amounts of boost and cut desired. The gain
expressions of Figure B1 indicate that the slope of the 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.:
Bass Circuit: A LOW ( Boost ) = 10A MID
Ie = IS e
qV be
--------------- – 1
KT
(A5)
Using the values shown in Figure 14 plus data on the
2N6292 (a typical transistor that could be used in the circuit),
the dynamic impedance of the circuit at a total current of
40mA is found to be 4.6Ω. In the actual design of the Vbe
multiplier, the value of IR2 must be greater than Vbe or the
transistor will never become forward biased.
Appendix B - Tone Controls
Figure B1 shows four operational amplifier circuit configurations and the gain expressions for each. The asymptotic low
frequency gain is obtained by letting S approach zero in
each case:
A MID
A LOW ( Cut ) = ---------------10
Treble Circuit: A HIGH ( Boost ) = 10A MID
A MID
A HIGH ( Cut ) = ---------------10
then the following relationships result:
Bass Circuit: R1 = 10R2
R3 = 99R2
Treble Circuit: C1 = 10C4
10C4
C2 = --------------99
Treble Circuit: C1 = 10C4
10C4
C2 = --------------99
8
Application Note 6077
C1
C1
R2
R1
R3
R3
R1
R2
-
-
EO
+
EO
+
ES
ES
( R2R3 + R1R3 )
1 + SC 2 -------------------------------------------R1 + R2 + R3
( R1 + R2 + R3 )
A =  ------------------------------------- ------------------------------------------------------------------ R2 + R3 
R2R3
1 + SC2  ----------------------
 R2 + R3
( R2R3 + R1R3 )
R1 + R2 + R3
A =  ------------------------------------- 1 + SC 1 ------------------------------------------( R1 + R2 + R3 )


R2
------------------------------------------------------------------1 + SR3C1
R1 + R2 + R3
A LOW FREQUENCY = ------------------------------------R2
R1 + R2 + R3
A LOW FREQUENCY = ------------------------------------R2 + R3
FIGURE B1 (A). BASS BOOST
FIGURE B1 (B). BASS CUT
C3
C3
C1
C4
-
C4
REFF
+
C1
REFF
EO
-
+
EO
ES
ES
( C1 C4 + C3 C4 + C1 C3 )
C1 + C4 1 + SR EFF -------------------------------------------------------------------------( C1 + C4 )
A =  ----------------------
 C4  --------------------------------------------------------------------------------------------------------1 + SR EFF C3
( C1 C4 + C2 C4 + C1 C2 )
C1 + C4 1 + SR EFF -------------------------------------------------------------------------( C1 + C4 )
A =  ----------------------
 C4  --------------------------------------------------------------------------------------------------------1 + SR EFF ( C1 + C2 )
C1 + C4
A LOW FREQUENCY = ---------------------C4
C1 + C4
A LOW FREQUENCY = ---------------------C4
FIGURE B1 (C). TREBLE BOOST
FIGURE B1 (D). TREBLE CUT
FIGURE B1. FOUR OPERATIONAL AMPLIFIER CIRCUIT CONFIGURATIONS AND THE GAIN EXPRESSIONS FOR EACH
The unaffected portion of the gain (A high for the bass control and A low for the treble control) is 11 in each case.
To make the controls work symmetrically, the low and high
frequency break points must be equal for both boost and cut.
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
Thus:
C1 R3 ( R1 + R2 )
R2 R3
Bass Control: ---------------------------------------------- = C2
-------------------------R1 + R2 + R3
R2 + R3
R3 ( R1 + R2 )
and C1 R3 = C2
---------------------------------------------R1 + R2 + R3
since R3 ≅ R2 + R3, C2 = 10C1
( C1 C4 + C3 C4 + C1 C3 )
Treble Control: R1 -------------------------------------------------------------------------C1 + C4
R1 R2
= ---------------------- ( C1 + C2 )
R1 + R2
and
since
R1 R2 ( C1 C4 + C2 C4 + C1 C2 )
R2C3 =  ---------------------- ------------------------------------------------------------------------- R1 + R2
( C1 + C4 )
9
1
0.1C1R1 = -------------------------2π × 1000
and for the treble control
1
R1C3 = -------------------------2π × 1000
Response and Control Rotation
In a practical design, it is desirable to make “flat” response
correspond to the 50% rotation position of the control, and to
have an aural sensation of smooth variation of response on
either side of the mechanical center. It is easy to show that
the “flat” position of the bass control occurs when the wiper
are is advanced to 91% of its total resistance. The amplitude
response of the treble control is, however, never completely
“flat”; a computer was used to generate response curves as
controls were varied.
Application Note 6077
CW
R3
CCW
R1
15K
0.001µF
1K
45
0.2
µF
Q = 1.0
40
0.01µF
0.001
µF
1.8K P
EO/ES (dB)
R2
68Ω 0.12µF
ES
820Ω
±
Figure B3 is a plot of the response with bass and treble tone
controls combined at various settings of both controls. The
values shown are the practical ones used in the actual
design. Figure B4 shows the information of Figure B3 replotted as a function of electrical rotation. The ideal taper for
each control would be the complement of the 100Hz plot for
the bass control and the 10kHz response for the treble control. The mechanical center should occur at the crossover
point in each case.
EO
0.02
µF
Q
P = 1.0
35 Q = 0.99
100K
Q = 0.98
30
10K
P = 0.99
P = 0.98
P = 0.96
Q = 0.96
25
C2
Q =0 .914
20 Q = 0.85
C1
±
15
10
5
Q=0
0
10
FIGURE B2 (A). BASS CONTROL
Q = 0.75
Q = 0.5
Q = 0.2
100
P = 0.92
P = 0.8
P = 0.5
P = 0.3
P = 0.1
P = 0.05
1000
P=0
10K
100K
FREQUENCY (Hz)
C1
CW
R1
CCW
C4
R2
FIGURE B3. A PLOT OF THE RESPONSE OF THE CIRCUIT OF
FIGURE 14 WITH BASS AND TREBLE TONE CONTROLS COMBINE
45
C3
C2
40
±
35
FIGURE B2 (B). TREBLE CONTROL
FIGURE B2. CUT AND BOOST BASS AND TREBLE CONTROLS
THAT HAVE THE CHARACTERISTICS OF THE CIRCUITS IN FIGURE B1
GAIN (dB)
30
25
20
15
10
1000Hz
100Hz
31.6Hz
5
0
0.2
0.4
0.6
0.8
1.0
ELECTRICAL ROTATION OF BASS CONTROL
FIGURE B4 (A).
10
Application Note 6077
40
35
GAIN (dB)
30
25
1kHz
20
10kHz
15
31.6kHz
10
5
0
0.2
0.4
0.6
0.8
1.0
ELECTRICAL ROTATION OF TREBLE CONTROL
FIGURE B4 (B).
4. THE INFORMATION OF FIGURE B3 PLOTTED AS A FUNCTION OF ELECTRICAL ROTATION
References
[1] AN6668, “Applications of the CA3080 and CA3080A
High Performance Operational Transconductance Amplifiers,” H. A. Wittlinger, Harris Semiconductor.
[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.
11