AN6077: an IC Operational Transconductance Amplifier (OTA

An IC Operational Transconductance Amplifier

ODUCT (OTA) With Power Capability OBSOLETE PR ACEMENT MENDED REPL NO RECOM Application NoteTERSIL October 2000 AN6077.3 ations 1-888-IN ll Central Applic Ca [email protected] or email: centa

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

DEVIATION FROM STRAIGHT LINE DEVIATION FROM -0.8

sil shows the output current transfer characteristic of the NORMALIZED OUTPUTCURRENT AND -1.0 Corpo- amplifier. The shape of this characteristic remains constant -150 -100 -50 0 50 100 150 ration, and is independent of supply voltage. Only the maximum ΔVbe (mV) current is modified by the bias current. power FIGURE 3. THE OUTPUT CURRENT TRANSFER switch, CHARACTERISTIC OF THE OTA IS THE SAME 7 V+ AS THAT OF AN IDEALIZED DIFFERENTIAL power AMPLIFIER ampli- - 2 OTA The major controlling factor in the OTA is the input amplifier fier, bias current I ; as explained in Figure 1, the total output RIN ABC pro- 2RO ein current and gm are controlled by this current. In addition, the gram- gm ein 6 IOUT = gm (±ein) input bias current, input resistance, total supply current, and mable 2RO output resistance are all proportional to this amplifier bias 3 power + current. These factors provide the key to the performance of gm = 19.2 • IABC this most flexible device, an idealized differential amplifier, switch) (mS) (mA) ±IOUT ≈ IABC Max (mA) i.e., a circuit in which differential input to single ended output /Cre- RO ≈ 7.5/IABC 4 V- (mA) conversion can be realized. With this knowledge of the (MΩ)(mA) ator () 5 IABC 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

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 DIODE CURRENT = 0mA 6 realization of the ideal differential amplifier in which the full differential amplifier gm is converted to a single ended 5 100 output. Because the differential amplifier is ideal, its gm is IABC directly proportional to the operating current of the 4 500μA CA3080A 80 S/N RATIO differential amplifier; in the OTA the maximum output current 3 60 is equal to the amplifier bias current IABC. Thus, by varying

10μA (dB) S/N RATIO the amplifier bias current, the amplifier gain may be varied: THD (PERCENT) 2 40 A = gm RL where RL is the output load resistance. Figure 4 shows the basic configuration of the OTA DC gain control 1 20 THD circuit. 0 0 V +6V 0.1 1.0 10 100 1.0V X IO = gm VX AMPLITUDE SIGNAL 7 INPUT VOLTAGE (mV) INPUT MODULATED 2 - 51 OUTPUT FIGURE 5A. OTA IO CA3080A 6 7 DIODE CURRENT = 0.5mA 51 3 + 10K 6 4 5 -6V 5 100 IABC IABC 500μA CA3080A VM R 4 80 M S/N RATIO GAIN CONTROL 3 60 10μA S/N RATIO (dB) THD (PERCENT) 2 40 FIGURE 4. BASIC CONFIGURATION OF THE OTA DC GAIN THD CONTROL CIRCUIT 1 20

0 0 As long as the differential input signal to the OTA remains 1 10 100 1V 10V under 50mV peak-to-peak, the deviation from a linear INPUT VOLTAGE (mV) transfer will remain under 5 percent. Of course, the total FIGURE 5B. harmonic distortion will be considerably less than this value. 7 Signal excursions beyond this point only result in an DIODE CURRENT = 1mA undesired “compressed” output. The reason for this 6 compression can be seen in the transfer characteristic of the 5 100 differential amplifier in Figure 3. Also shown in Figure 3 is a curve depicting the departure from a linear line of this 4 80 500μA transfer characteristic. 3 60 The actual performance of the circuit shown in Figure 4 is IABC 10μA 2 40 CA3080A plotted in Figure 5. Both signal to noise ratio and total S/N RATIO (dB) THD (PERCENT) S/N THD harmonic distortion are shown as a function of signal input. 1 RATIO 20 Figures 5B and 5C show how the signal handling capability of 0 0 the circuit is extended through the connection of diodes on DISTORTION IS PRIMARILY the input as shown in Figure 6 [2]. Figure 7 shows total A FUNCTION OF SIGNAL INPUT system gain as a function of amplifier bias current for several 110 100 1V 10V values of diode current. Figure 8 shows an oscilloscope INPUT VOLTAGE (mV) reproduction of the CA3080 transfer characteristic as applied FIGURE 5C. to the circuit of Figure 4. The oscilloscope reproduction of FIGURE 5. PERFORMANCE CURVES FOR THE CIRCUIT OF Figure 9 was obtained with the circuit shown in Figure 6. Note FIGURES 4 AND 6

2 Application Note 6077

E IN 2K 100 0mA 1 10μA 2 2 E 51 O 100μA DIODE 3 CA3080A 6 10 CURRENT 0.5mA 4 10K 5 3 1mA 8 6 + 1.0

2K GAIN 7 14 DIODE 11 CURRENT 9 12 13 0.1

V-

0.01 Transistors from CA3046 array. 0 100 200 300 400 500 AGC System with extended input range. 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., I = 100μA ABC Horizontal: 0.5V/Div. Vertical: 50μA/Div., IABC = 100μA, Diode Current = 1mA

FIGURE 8. CA3080 TRANSFER CHARACTERISTIC FOR THE FIGURE 9. CA3080 TRANSFER CHARACTERISTIC FOR THE CIRCUIT OF FIGURE 4 CIRCUIT OF FIGURE 6

Simplified Differential Input to Single Ended Output Conversion One of the more exacting configurations for operational common mode range is that of the CA3080 differential 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 standard differential amplifier gm temperature coefficient of usually employed. The ratios of the resistors must be -0.3%/oC. Although the system of Figure 11 does not precisely matched to assure the desired common mode provide the precise gain control obtained with the standard rejection. Figure 11 shows another system using the operational amplifier approach, it does provide a good CA3080 to obtain this conversion without the use of simple compromise suitable for many differential transducer precision resistors. Differential input signals must be kept amplifier applications. under 126mV for better than 5 percent nonlinearity. The

3 Application Note 6077

R2 The CA3094

R1 The CA3094 offers a unique combination of characteristics DIFFERENTIAL - that suit it ideally for use as a programmable gain block for + OUTPUT INPUT audio power amplifiers. It is a transconductance amplifier in R3 R1 R3 R4 = 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

R4 R5 dissipation ratings sufficiently high to allow it to drive a + - complementary pair of transistors. For example, a 12W

R1 power amplifier stage (8Ω load) can be driven with peak currents of 35mA (assuming a minimum output transistor DIFFERENTIAL - R2 OUTPUT beta of 50) and supply voltages of ±18V. In this application, INPUT + the CA3094A is operated substantially below its supply

R3 R1 = R3 voltage rating of 44V max. and its dissipation rating of 1.6W - R4 R6 max. Also in this application, a high value of open-loop gain + = R R5 R7 suggests the possibility of precise adjustment of frequency 6 R 7 response characteristics by adjustment of impedances in the feedback networks.

+ - Implicit Tone Controls

R1 In addition to low distortion, the large amount of loop gain

R3 and flexibility of feedback arrangements available when DIFFERENTIAL R2 using the CA3094 make it possible to incorporate the tone INPUT R1 R4 = R2 R3 controls into the feedback network that surrounds the entire amplifier system. Consider the gain requirements of a

R4 phonograph playback system that uses a typical high quality - + OUTPUT 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 FIGURE 10. SOME TYPICAL DIFFERENTIAL TO SINGLE 10mV at 5cm/s. To get the desired output, the total system ENDED CONVERSION CIRCUITS 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 +V gain control. Figure 13 shows a system in which the tone IABC controls are implicit in the feedback circuits of the power amplifier. Both systems assume the same noise input voltage 500μA at the equalizer and main-amplifier inputs. The feedback 5 system shows a small improvement (3.8dB) in signal-to-noise ratio at maximum gain but a dramatic improvement (20dB) at 2K 7 the zero gain position. For purposes of comparison, the 3 + assumption is made that the tone controls are set “flat” in both DIFFERENTIAL CA3080 6 OUTPUT INPUT 2K cases. 2 - 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 g ≈ 10mS. m supply rejection and common-mode rejection are 90dB and ∴ A = 10mS x 10K = 100. 100dB, respectively. An amplifier with 40dB of gain and 90dB FIGURE 11. A DIFFERENTIAL TO SINGLE ENDED of power supply rejection would require 316mV of power CONVERSION CIRCUIT WITHOUT PRECISION supply ripple to produce 1mV of hum at the output. Thus, no RESISTORS further filtering is required other than that given by the energy storage capacitor at the output of the rectifier system.

4 Application Note 6077

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

EQUALIZER TONE VOLUME BUFFER STAGE POWER AREF = 32dB CONTROLS -6 -6 CONTROLS EN AT INPUT = 5 x 10 AMP EN AT INPUT = 1 x 10 -20dB 8Ω SPEAKER PICKUP -6 -6 -6 -3 ESIG =1mV EN = 40 x 10 EN = 4 x 10 EN = 4 x 10 EN = 6.23 x 10 EO 4 = = 640 AT MAX VOL TOTAL GAIN = 72dB -3 EN 6.23 x 10 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 AMPLIFIER WITH FEED- VOLUME AREF = 32dB BACK TONE CONTROLS -6 CONTROLS -6 EN AT INPUT = 1 x 10 EN = 5 x 10 PICKUP E =1mV SIG -6 -6 -3 EN = 40 x 10 EN = 40 x 10 EN = 4.03 x 10 EO 4 =-3 = 990 AT MAX VOL EN 4.03 x 10

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 V multiplier with a A complete power amplifier using the CA3094 and three be 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 V The amplifier is shown in a single-channel configuration, but be 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 The tone controls, the essential elements of the feedback “bootstrap” arrangement. Capacitor C3 provides added base system, are located in two sets of parallel paths. The bass drive for Q during positive excursions of the output. The 1 network includes R3, R4, R5, C4, and C5. C6 blocks the DC circuit can be operated from a single power supply as well as from the feedback network so that the DC gain from input to the from a split supply as shown in Figure 15. The changes feedback takeoff point is unity. The residual DC output voltage required for 14.4V operation with a 3.2Ω speaker are also at the speaker terminals is then indicated in the diagram. ⎛⎞R11 + R12 ⎜⎟R1------IABC The amplifier may also be modified to accept input from ⎝⎠R12 ceramic phonograph cartridges. For standard inputs where R is the source resistance. The input bias current is (equalizer preamplifiers, tuners, etc.) C1 is 0.047μF, R1 is 1 then 250kΩ, and R2 and C2 are omitted. For ceramic-cartridge IABC ()VCC – VBE inputs, C1 is 0.0047μF, R1 is 2.5MΩ, and the jumper across ------= –------2β 2βR C2 is removed. 6 Output Biasing The treble network consists of R7, R8, R9, R10, C7, C8, C9, and C . Resistors R and R limit the maximum available cut Instead of the usual two-diode arrangement for establishing 10 7 9 and boost, respectively. The boost limit is useful in curtailing idling currents in Q and Q , a “V Multiplier”, transistor Q , is 1 2 be 3 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 Q and the base of Q at a constant multiple of the 1 2 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

R C R 120V AC TO “BOOST” 20 “CUT” 7 7 T (CW) 15K 0.01μF 820Ω 1 26.8VCT AT 1A C10 (CCW) + 4700μF D1 0.12μF R8 TREBLE - 1800Ω D2 120V AC C8 R9 220Ω C3 1W 68Ω C9 15μF 0.001μF 5600Ω + 0.001μF 220Ω D 1W 3 5μF - + Q1 - 2N6292 4700 D + μF 4 30Ω 0.47Ω C1 7 3pF Q E 3 S 1 2N6292 0.47Ω R1 2 - 27Ω R11 330Ω Q CA3094 8 2 2N6107 3 + R 6 12 47Ω R2 4 1.8MΩ 5 1Ω R6 680K 0.47 μF

C5 0.2μF C C R5 4 C2 6 0.02μF 25μF 1K BASS 0.47μF + - “BOOST” R4 “CUT” R3 (CW) 100K(CCW) 10K JUMPER

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

+36V VCC

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

68 0.01μF R2 15μF + 220Ω

1.8K - 1W 820 5μF Q1 2N6292 0.001μF R3 30Ω 0.47Ω 1500μF Q + - 5 3 0.22μF 2N6292 7 R4 100K 2 27Ω 330 0.47Ω Ω

220K CA3094 8 + 6 3 Q2 47Ω

25μF - 1 2N6107 1/2VCC 4 1Ω 0.47μF 220K 25μF 5% 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 2.0 Figure 16 is a plot of the measured response of the complete 1.8 amplifier at the extremes of tone control rotation. A 1.6 comparison of Figure 16 with the computed curves of Figure 1.4 B4 (Appendix B) shows good agreement. The total harmonic distortion of the amplifier with an unregulated power supply is 1.2 shown in Figure 17; IM distortion is plotted in Figure 18. Hum 1.0 60Hz 2kHz and noise are typically 700μV at the output, or 83dB down. 0.8 60Hz 7kHz 60Hz 12kHz 60 0.6 BASS BOOST TREBLE BOOST 55 0.4 50 0.2 INTERMODULATION DISTORTION (%) 45 FLAT 0 2 4 6 8 10 12 14 40 OUTPUT POWER (W) (dB) 35 S /E

O 30 FIGURE 18. IM DISTORTION OF THE AMPLIFIER WITH AN E 25 UNREGULATED SUPPLY TREBLE CUT 20 BASS CUT Companion RlAA Preamplifier 15 Many available preamplifiers are capable of providing the 10 2368 2368 2368 2368 drive for the power amplifier of Figure 14. Yet the unique 10 100 1000 10K 100K characteristics of the amplifier, its power supply, input FREQUENCY (Hz) impedance, and gain make possible the design of an RIAA FIGURE 16. THE MEASURED RESPONSE OF THE AMPLIFIER preamplifier that can exploit these qualities. Since the input AT EXTREMES OF TONE CONTROL ROTATION impedance of the amplifier is essentially equal to the value of the volume control resistance (250kΩ), the preamplifier need 1.0 not have high output current capability. Because the gain of 1kHz 0.9 the power amplifier is high (40dB) the preamplifier gain only 2kHz 26kHz has to be approximately 30dB at the reference frequency 0.8 (1kHz) to provide optimum system gain. 0.7

0.6 16kHz Figure 19 shows the schematic diagram of a CA3080 preamplifier. The CA3080, a low cost OTA, provides 0.5 4kHz sufficient open-loop gain for all the bass boost necessary in 0.4 RIAA compensation. For example, a gm of 10mS with a load 0.3 26kHz resistance of 250kΩ provides an open-loop gain of 68dB, 16kHz thus allowing at least 18dB of loop gain at the lowest 0.2 1kHz frequency. The CA3080 can be operated from the same TOTAL HARMONIC DISTORTION (%) 0.1 4kHz power supply as the main amplifier with only minimal 0 24681012 decoupling because of the high power supply rejection OUTPUT POWER (W) inherent in the device circuitry. In addition, the high voltage swing capability at the output enables the CA3080 FIGURE 17. TOTAL HARMONIC DISTORTION OF THE AMPLIFIER WITH AN UNREGULATED POWER preamplifier to handle badly over modulated (over-cut) SUPPLY 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).

7 Application Note 6077

120K The derivative of Equation A1 with respect to I yields the V+ incremental impedance of the Vbe multiplier: 5.6K 0.002μF 680pF dE1 R1 BR K R ------==Z ------+ 1 3 2 (EQ. A3) dI β + 1 1 + ------1.5M ()β + 1 R2 R2Ie + K3 + 50μF 3.9K 7 - 2 - 5μF CA3080 6 where K3 is a constant of the transistor Q1 and can be found 1μF EOUT from: 3 + 4 Vbe = K3lnIe – K2 ES 56K (EQ. A4) 5

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

V- qVbe (EQ. A5) 120K ------– 1 KT Ie = ISe

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

Appendix A - Vbe Multiplier R1 ++R2 R3 Bass Boost: A = ------The equivalent circuit for the Vbe multiplier is shown in LOW R Figure A1. The voltage E1 is given by: 2 R1 ++R2 R3 Bass Cut: A = ------LOW R + R R1I R 2 3 E = ------+ V 1 (EQ. A1) 1 β + 1 be 1 + ------C + C R2()β + 1 1 4 Treble Boost: ALOW = ------C4

C + C E1 1 4 Treble Cut: ALOW = ------C4

R1 The asymptotic high-frequency gain is obtained by letting S I increase without limit in each expression: Vbe R1 + R2 Bass Boost: AHIGH = ------R2 R I 2 e R1 + R2 Bass Cut: AHIGH = ------R2 ⎛⎞C + C FIGURE A1. EQUIVALENT CIRCUIT FOR THE Vbe MULTIPLIER 3 4 Treble Boost: AHIGH = 1C+ 1⎜⎟------⎝⎠C3C4 The value of Vbe is itself dependent on the emitter current of C1C4 the transistor, which is, in turn, dependent on the input C + ------2 + current I since: C1 C4 Treble Cut: AHIGH = ------C1 + C2 V be (EQ. A2) Ie = I – ------R2

8 Application Note 6077

Note that the expressions for high frequency gain are : = identical for both bass circuits, while the expressions for low Bass Circuit: ALOW() Boost 10AMID frequency gain are identical for the treble circuits. A A = ------MID LOW() Cut 10 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 AMID AHIGH() Cut = ------the parallel combination of R1 and R2 of Figure B2 when the 10 control is rotated to its maximum counterclockwise position. then the following relationships result:

When the control is rotated to its maximum clockwise Bass Circuit: R1 = 10R2 position, the value is equal to R1. R3 = 99R2 To compute the circuit constants, it is necessary to decide in Treble Circuit: C = 10C advance the amounts of boost and cut desired. The gain 1 4 10C4 expressions of Figure B1 indicate that the slope of the C = ------2 99 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.

C1 C2 R2 R1

R3 R1 R3 - R2 - + EO + EO

ES ES

()R R + R R ()R2R3 + R1R3 2 3 1 3 ⎛⎞R ++R R 1SC+ ------1SC+ ------1 2 3 1 R ++R R 2 ()R ++R R A = ⎜⎟------()R1 ++R2 R3 ⎛⎞1 2 3 1 2 3 ⎝⎠R ------A = ⎜⎟------2 R + R 1SR+ 3C1 ⎝⎠2 3 ⎛⎞R2R3 1SC2+ ⎜⎟------⎝⎠R2 + R3 R1 ++R2 R3 ALOW FREQUENCY = ------R ++R R R2 1 2 3 ALOW FREQUENCY = ------R2 + R3 FIGURE B1 (A). BASS BOOST FIGURE B1 (B). BASS CUT

C3 C2 C1 C4 C4

REFF C REFF - 1 - + EO + EO

ES ES

()C C ++C C C C ()C C ++C C C C ⎛⎞C + C 1 4 3 4 1 3 ⎛⎞C + C 1 4 2 4 1 2 1 4 1SR+ EFF------1 4 1SR+ EFF------A = ⎜⎟------()C1 + C4 A = ⎜⎟------()C1 + C4 ⎝⎠C4 ------⎝⎠C4 ------1SR+ EFFC3 1SR+ EFF()C1 + C2 C1 + C4 C1 + C4 ALOW FREQUENCY = ------ALOW FREQUENCY = ------C4 C4 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. To make the controls work symmetrically, the low and high frequency break points must be equal for both boost and cut. C2 C1 Thus: - + C1R3()R1 + R2 C2R2R3 Bass Control:------= ------R1 ++R2 R3 R2 + R3

C2R3()R1 + R2 and C R = ------1 3 R ++R R 1 2 3 FIGURE B2 (A). BASS CONTROL since R3 ≅ R2 + R3,C2 = 10C1

()C1C4 ++C3C4 C1C3 Treble Control: R1------C1 + C4 C1 CW R1 CCW C4

R2 R1R2 = ------()C1 + C2 R1 + R2 ⎛⎞R R ()C C ++C C C C C3 and 1 2 1 4 2 4 1 2 R2C3 = ⎜⎟------C2 ⎝⎠R1 + R2 ()C1 + C4 - + 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: 1 for the base control 0.1C R = ------FIGURE B2 (B). TREBLE CONTROL 1 3 2π × 1000 1 FIGURE B2. CUT AND BOOST BASS AND TREBLE CONTROLS and for the treble control R C = ------1 3 2π × 1000 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 68Ω 0.12μF 15K 0.01μF have an aural sensation of smooth variation of response on P 0.001 either side of the mechanical center. It is easy to show that 1.8K μF 820Ω the “flat” position of the bass control occurs when the wiper arm is advanced to 91% of its total resistance. The 0.001μF - ES + EO amplitude response of the treble control is, however, never 0.2 45 1K μF 0.02 completely “flat”; a computer was used to generate response μF Q = 1.0 curves as controls were varied. 40 Q ) Q = 0.99 P = 1.0

dB 35

Figure B3 is a plot of the response with bass and treble tone (

100K 10K S Q = 0.98 P = 0.99 controls combined at various settings of both controls. The E / 30 P = 0.98 O values shown are the practical ones used in the actual E Q = 0.96 P = 0.96 25 design. Figure B4 shows the information of Figure B3 Q =0.914 replotted as a function of electrical rotation. The ideal taper 20 Q = 0.85 for each control would be the complement of the 100Hz plot 15 for the bass control and the 10kHz response for the treble P = 0.92 P = 0.8 10 control. The mechanical center should occur at the Q = 0.75 P = 0.5 crossover point in each case. Q = 0.5 P = 0.3 5 P = 0.1 P = 0 Q = 0.2 Q = 0 P = 0.05 0 10 100 1000 10K 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

10 Application Note 6077

45 40

40 35 35 30 30 25 25 1kHz 20 20 1000Hz 10kHz GAIN (dB) GAIN (dB) GAIN 15 31.6kHz 15 100Hz 10 10 31.6Hz

5 5

0 0 0.2 0.4 0.6 0.8 1.0 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 A FUNCTION OF ELECTRICAL ROTATION For Intersil documents available on the internet, see web site 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.

All Intersil semiconductor products are manufactured, assembled and tested under ISO9000 quality systems certification. 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