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OB ENT DED REPLACEM NO RECOMMEN Application Note L RSI ations 1-888-INTE all Central Applic p@intersil.com C or email: centap
An IC Operational Transconductance Amplifier (OTA) With Power Capability CT SOLETE PRODU
October 2000 AN6077.3
[ /Title (AN60 77) /Subject (An IC Operational Transc onductance Amplifier (OTA) With Power Capability) /Autho r () /Keywords (Intersil Corporation, power switch, power amplifier, programmable power switch) /Creator ()
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.
7
V+
Y
Z OUTPUT
INVERTING INPUT AMPLIFIER BIAS CURRENT
2
Q1 Q2
3
NON-INVERTING INPUT
6
5 IABC
W
X
4
V-
FIGURE 2. CURRENT MIRRORS W, X, Y AND Z USED IN THE OTA
What Is an 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 2 RIN V+ OTA 1.0 NORMALIZED OUTPUT CURRENT AND DEVIATION FROM STRAIGHT LINE 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1.0 -150 -100 -50 0 50 Vbe (mV) 100 150 DIFFERENTIAL AMPLIFIER TRANSFER CHARACTERISTIC
FIGURE 3. THE OUTPUT CURRENT TRANSFER CHARACTERISTIC OF THE OTA IS THE SAME AS THAT OF AN IDEALIZED DIFFERENTIAL AMPLIFIER
ein gm ein
2RO 6 2RO IOUT = gm (ein)
3
+ gm = 19.2 * IABC (mS) (mA) 4 V5 IABC RO 7.5/IABC (M) (mA) IOUT IABC Max (mA) (mA)
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.
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 4-1
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(c) Intersil Corporation 2000
Application Note 6077
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 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. 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.
VX SIGNAL INPUT 51 7 2 +6V IO = gm VX AMPLITUDE MODULATED OUTPUT
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.
7 DIODE CURRENT = 0mA 6 5 4 3 10A 2 1 THD 0 0.1 0 1.0 10 INPUT VOLTAGE (mV) 100 1.0V 40 20 500A IABC CA3080A S/N RATIO 100 80 60 S/N RATIO (dB) S/N RATIO (dB) S/N RATIO (dB)
OTA CA3080A 6 IO 10K 4 5 -6V IABC
THD (PERCENT)
FIGURE 5A.
7 DIODE CURRENT = 0.5mA 6 5 4 3 10A 2 40 THD 20 0 1 10 100 INPUT VOLTAGE (mV) 1V 10V 500A IABC CA3080A S/N RATIO 100 80 60
51
3
+
VM GAIN CONTROL
RM
FIGURE 4. BASIC CONFIGURATION OF THE OTA DC GAIN CONTROL CIRCUIT
THD (PERCENT)
1 0
THD (PERCENT)
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. 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 4-2
FIGURE 5B.
7 DIODE CURRENT = 1mA 6 5 4 3 2 1 0 DISTORTION IS PRIMARILY A FUNCTION OF SIGNAL INPUT 1V 100 1 10 INPUT VOLTAGE (mV) 10V IABC CA3080A S/N RATIO 10A THD 20 0 500A 100 80 60 40
FIGURE 5C. FIGURE 5. PERFORMANCE CURVES FOR THE CIRCUIT OF FIGURES 4 AND 6
Application Note 6077
EIN 2K 51 2 1 3 4 5 8 2K 7 11 9 12 14 13 V0.01 0 100 200 300 400 IABC (A) 500 DIODE CURRENT 0.1 6 3 + 2 CA3080A 6 10K GAIN 1.0 EO 10 0.5mA 1mA 100 0mA 10A 100A DIODE CURRENT
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
FIGURE 7. TOTAL SYSTEM GAIN vs AMPLIFIER BIAS CURRENT FOR SEVERAL VALUES OF DIODE CURRENT
Horizontal: 25mV/Div. Vertical: 50A/Div., IABC = 100A
Horizontal: 0.5V/Div. Vertical: 50A/Div., IABC = 100A, Diode Current = 1mA FIGURE 9. CA3080 TRANSFER CHARACTERISTIC FOR THE CIRCUIT OF FIGURE 6
FIGURE 8. CA3080 TRANSFER CHARACTERISTIC FOR 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 with the standard operational amplifier approach, it does provide a good simple compromise suitable for many differential transducer amplifier applications.
4-3
Application Note 6077
R2 R1 DIFFERENTIAL INPUT R3 + R4 OUTPUT R1 R =3 R2 R4
The CA3094
The CA3094 offers a unique combination of characteristics that suit it ideally for 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 (8 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.
+ -
R4 R1
R5
DIFFERENTIAL INPUT
R2 R3 + R6
+
OUTPUT R1 = R3 R4 R5 = R6 R7
R7
+ R1 DIFFERENTIAL INPUT R2 R3 R1 R2 R4 OUTPUT = R4 R3
Implicit Tone Controls
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. 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.
+
FIGURE 10. SOME TYPICAL DIFFERENTIAL TO SINGLE ENDED CONVERSION CIRCUITS
+V IABC
500A 5 2K 3 DIFFERENTIAL INPUT 2K 2 + CA3080 6 4 VOUTPUT RL 10K 7
-
Cost Advantages
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.
A = gm RL at 500A, IABC: gm 10mS. A = 10mS x 10K = 100. FIGURE 11. A DIFFERENTIAL TO SINGLE ENDED CONVERSION CIRCUIT WITHOUT PRECISION RESISTORS
4-4
Application Note 6077
ESIG = 40mV ESIG = 4mV ESIG = 4mV ATOTAL = 60dB EQUALIZER AREF = 32dB EN AT INPUT = 1 x 10-6 PICKUP ESIG =1mV EN = 40 x 10-6 TONE CONTROLS -20dB EN = 4 x 10-6 TOTAL GAIN = 72dB VOLUME CONTROLS EN = 4 x 10-6 BUFFER STAGE EN AT INPUT = 5 x 10-6 POWER AMP 8 SPEAKER EN = 6.23 x 10-3 EO = 4V
= 640 AT MAX VOL 6.23 x 10-3 EN EN = 4mV AT MIN VOL
EO
4 =
FIGURE 12. BLOCK DIAGRAM OF A SYSTEM USING A "LOSSER" TYPE TONE CONTROL CIRCUIT
ESIG = 40mV ESIG = 40mV ATOTAL = 60dB EQUALIZER AREF = 32dB EN AT INPUT = 1 x 10-6 PICKUP ESIG =1mV EN = 40 x 10-6 VOLUME CONTROLS AMPLIFIER WITH FEEDBACK TONE CONTROLS EN = 5 x 10-6 EN = 4.03 x 10-3 = 990 AT MAX VOL EO = 4V
EN = 40 x 10-6
EO EN
4 =
4.03 x 10-3
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 3.2 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 0.047F, R1 is 250k, and R2 and C2 are omitted. For ceramic-cartridge inputs, C1 is 0.0047F, R1 is 2.5M, and the jumper across C2 is removed.
A bias arrangement that can be accomplished at lower cost than those already described replaces the Vbe multiplier with a 1N5391 diode in series with an 8.2 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
R 11 + R 12 R 1 -------------------------- I ABC R 12
where R1 is the source resistance. The input bias current is then
I ABC ( V CC - V BE ) ------------ = - --------------------------------2 2R 6
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.
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 3H inductor (1A) in parallel with a 22 resistor is adequate. The derivation of circuit constants is shown in Appendix B. Curves of control action versus electrical rotation are also given.
4-5
Application Note 6077
"BOOST" R20 (CW) 15K R8 TREBLE 1800 C8 C9 0.001F 0.001F 5600 5F + 220 1W Q1 2N6292 30 7 1 R1 2 3pF 27 8 6 4 5 R6 680K 0.47 F 1 Q3 2N6292 0.47 Q2 2N6107 R11 330 0.47 C7 R7 "CUT" (CCW) 0.01F 820 120V AC TO 26.8VCT AT 1A
C10
T1 +
0.12F R9 68
220 1W C3 15F +
4700F
D1 D2 120V AC
D3
C1 ES
+
4700 F
D4
CA3094
3
+
R12 47
R2 1.8M
C5 0.2F C6 25F + R5 1K C4 0.02F R3 10K C2 0.47F
BASS "BOOST" R4 (CW) 100K
-
"CUT" (CCW)
JUMPER
FIGURE 14. A COMPLETE POWER AMPLIFIER USING THE CA3094 AND THREE ADDITIONAL TRANSISTORS
+36V VCC R5 1.2M 0.01F 1.8K 820 0.001F 5 2 220K 3 1 4 0.02F 100K BASS 10K 1 + 7 CA3094 6 8 R4 27 5F + R1 220 1W +
220K 5% 68
0.12F
TREBLE 15K
5.6K
-
R2 15F 220 1W R3 30
Q1 2N6292 1500F +330
0.22F 100K
0.47 Q3 2N6292 0.47 Q2 2N6107
25F 1/2VCC 0.2F
47 0.47F
220K 5%
25F 1/2VCC -+
3pF 47K
1K
FIGURE 15. A POWER AMPLIFIER OPERATED FROM A SINGLE SUPPLY
4-6
Application Note 6077
Performance
INTERMODULATION DISTORTION (%) 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 2 4 6 8 10 12 14 60Hz 60Hz 60Hz 2kHz 7kHz 12kHz
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 700V at the output, or 83dB down.
60 55 50 45 EO /ES (dB) 40 35 30 25 20 15 10 2 10 3 68 2 100 3 68 2 1000 3 68 2 10K 3 68 100K BASS CUT TREBLE CUT FLAT BASS BOOST TREBLE BOOST
OUTPUT POWER (W)
FIGURE 18. IM DISTORTION OF THE AMPLIFIER WITH AN UNREGULATED SUPPLY
Companion RlAA Preamplifier
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 (250k), 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. Figure 19 shows the schematic diagram of a CA3080 preamplifier. The CA3080, a low cost OTA, provides sufficient open-loop gain for all the bass boost necessary in RIAA compensation. For example, a gm of 10mS with a load resistance of 250k 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).
FREQUENCY (Hz)
FIGURE 16. THE MEASURED RESPONSE OF THE AMPLIFIER AT EXTREMES OF TONE CONTROL ROTATION
1.0 TOTAL HARMONIC DISTORTION (%) 0.9 2kHz 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 4kHz 0 2 4 6 8 10 12 1kHz 26kHz 16kHz 4kHz OUTPUT POWER (W) 16kHz 26kHz 1kHz
FIGURE 17. TOTAL HARMONIC DISTORTION OF THE AMPLIFIER WITH AN UNREGULATED POWER SUPPLY
4-7
Application Note 6077
120K V+ 5.6K 0.002F 680pF 1.5M 3.9K 5F 1F 3 ES 56K 5 56K 5.6K V120K 2 7 CA3080 + 4 6 EOUT +
The derivative of Equation A1 with respect to I yields the incremental impedance of the Vbe multiplier:
R1 dE 1 K3 R2 BR 1 ---------- = Z = ------------ + 1 + ------------------------- ------------------------dI +1 ( + 1 )R 2 R 2 I e + K 3
50F
(EQ. A3)
-
where K3 is a constant of the transistor Q1 and can be found from:
V be = K 3 lnI e - K 2 (EQ. A4)
Equation A4 is but another form of the diode equation:
qV be -------------- - 1 KT
(EQ. A5)
Ie = IS e
0.002F 680pF 1.5M 3.9K 2 + 5F 1F 3 ES 56K 5 56K 7 CA3080 + 4 6 EOUT
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 4.6. 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.
+
50F
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:
R1 + R2 + R3 Bass Boost: A LOW = ---------------------------------R2 R1 + R2 + R3 Bass Cut: A LOW = ---------------------------------R2 + R3 C1 + C4 Treble Boost: A LOW = -------------------C4
FIGURE 19. A CA3080 PREAMPLIFIER
Appendix A - Vbe Multiplier
The equivalent circuit for the Vbe multiplier is shown in Figure A1. The voltage E1 is given by:
R1 I R1 E 1 = ------------ + V be 1 + ------------------------+1 R ( + 1)
2
(EQ. A1)
E1 R1 I Vbe
C1 + C4 Treble Cut: A LOW = -------------------C4
The asymptotic high-frequency gain is obtained by letting S increase without limit in each expression:
R1 + R2 Bass Boost: A HIGH = -------------------R2
R2
Ie
R1 + R2 Bass Cut: A HIGH = -------------------R2 C 3 + C 4 Treble Boost: A HIGH = 1 + C 1 -------------------- C3 C4 C1 C4 C 2 + -------------------C1 + C4 Treble Cut: A HIGH = ---------------------------------C1 + C2
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:
V be I e = I - --------R2 (EQ. A2)
4-8
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. 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 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: R 1 = 10R 2 R 3 = 99R 2 Treble Circuit: C 1 = 10C 4 10C 4 C 2 = ------------99
C1 R2 R3
C2 R1
+
ES
R1 EO
R2
R3 + ES
-
EO
( R2 R3 + R1 R3 ) R 1 + R 2 + R 3 1 + SC ----------------------------------------1 ( R + R + R )A = ---------------------------------- 1 2 3 R2 --------------------------------------------------------------1 + SR 3 C 1 R1 + R2 + R3 A LOW FREQUENCY = ---------------------------------R2 FIGURE B1 (A). BASS BOOST
C3 C1 C4
( R2 R3 + R1 R3 ) 1 + SC 2 ----------------------------------------( R1 + R2 + R3 ) R 1 + R 2 + R 3 A = ---------------------------------- -------------------------------------------------------------- R2 + R3 R2 R3 1 + SC2 -------------------- R 2 + R 3 R1 + R2 + R3 A LOW FREQUENCY = ---------------------------------R2 + R3 FIGURE B1 (B). BASS CUT
C2 C4 C1 EO ES REFF
+ ES
-
REFF
+
-
EO
( C1 C4 + C3 C4 + C1 C3 ) C 1 + C 4 1 + SR EFF --------------------------------------------------------------A = -------------------- ( C1 + C4 ) C 4 --------------------------------------------------------------------------------------------1 + SR EFF C 3 C1 + C4 A LOW FREQUENCY = -------------------C4 FIGURE B1 (C). TREBLE BOOST
( C1 C4 + C2 C4 + C1 C2 ) C 1 + C 4 1 + SR EFF --------------------------------------------------------------A = -------------------- ( C1 + C4 ) C 4 --------------------------------------------------------------------------------------------1 + SR EFF ( C 1 + C 2 ) C1 + C4 A LOW FREQUENCY = -------------------C4 FIGURE B1 (D). TREBLE CUT
FIGURE B1. FOUR OPERATIONAL AMPLIFIER CIRCUIT CONFIGURATIONS AND THE GAIN EXPRESSIONS FOR EACH
4-9
Application Note 6077
The unaffected portion of the gain (AHIGH for the bass control and ALOW 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. Thus:
C1 R3 ( R1 + R2 ) C2 R2 R3 Bass Control: ----------------------------------------- = ---------------------R1 + R2 + R3 R2 + R3
R2 CW R3 CCW R1
C2 C1 +
-
C2 R3 ( R1 + R2 ) and C 1 R = ----------------------------------------3 R1 + R2 + R3
since R3 R2 + R3, C2 = 10C1
( C1 C4 + C3 C4 + C1 C3 ) Treble Control: R 1 --------------------------------------------------------------C +C
1 4
FIGURE B2 (A). BASS CONTROL
C1
CW R2
R1
CCW
C4
R1 R2 = -------------------- ( C 1 + C 2 ) R1 + R2
12 14 24 12 and R 2 C 3 = -------------------- ---------------------------------------------------------------
R R (C C + C C + C C ) ( C1 + C4 ) R 1 + R 2
C3 C2 +
-
since C 1 100C 2 , C 2 = C 3 and C 1 = 10C 4 , R 1 = 9R 2 To make the controls work in the circuit of Figure 14, breaks were set at 1000Hz:
1 for the base control 0.1C 1 R 3 = -------------------------2 x 1000 1 and for the treble control R 1 C 3 = -------------------------2 x 1000
FIGURE B2 (B). TREBLE CONTROL FIGURE B2. CUT AND BOOST BASS AND TREBLE CONTROLS THAT HAVE THE CHARACTERISTICS OF THE CIRCUITS IN FIGURE B1
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 arm 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.
EO/ES (dB)
68 0.12F
15K 1.8K P 0.001 F
0.01F
820 +
0.001F 45 40 Q = 1.0 Q 1K 0.2 F
ES 0.02 F
-
EO
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.
35 Q = 0.99 30 25 Q =0.914 20 Q = 0.85 15 10 5 0 10 Q=0 100 Q = 0.98 Q = 0.96
P = 1.0 100K P = 0.98 P = 0.96 10K P = 0.99
Q = 0.75 Q = 0.5 Q = 0.2
P = 0.92 P = 0.8 P = 0.5 P = 0.3 P = 0.1 P = 0.05 1000 10K
P=0
100K
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
4-10
Application Note 6077
45 40 35 30 GAIN (dB) GAIN (dB) 25 20 15 10 5 0 0.2 0.4 0.6 0.8 1.0 ELECTRICAL ROTATION OF BASS CONTROL 1000Hz 100Hz 31.6Hz 40 35 30 25 1kHz 20 15 10 5 0 0.2 0.4 0.6 0.8 1.0 10kHz 31.6kHz
ELECTRICAL ROTATION OF TREBLE CONTROL
FIGURE B4 (A).
FIGURE B4 (B). FIGURE B4. THE INFORMATION OF FIGURE B3 PLOTTED AS A FUNCTION OF ELECTRICAL ROTATION
References
For Intersil documents available on the internet, see web site http://www.intersil.com/ Intersil AnswerFAX (321) 724-7800. [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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Intersil semiconductor products are sold by description only. Intersil Corporation reserves the right to make changes in circuit design and/or specifications at any time without notice. Accordingly, the reader is cautioned to verify that data sheets are current before placing orders. Information furnished by Intersil is believed to be accurate and reliable. However, no responsibility is assumed by Intersil or its subsidiaries for its use; nor for any infringements of patents or other rights of third parties which may result from its use. No license is granted by implication or otherwise under any patent or patent rights of Intersil or its subsidiaries. For information regarding Intersil Corporation and its products, see web site http://www.intersil.com
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