OB ENT DED REPLACEM Note NO RECOMMEN Application INTERSIL lications 1-888- m pp A al tr en C l al C [email protected] or email: centap 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. October 2000 AN6077.3 7 V+ Y Z OUTPUT INVERTING INPUT AMPLIFIER BIAS CURRENT 2 Q1 Q2 5 W 3 NON-INVERTING INPUT 6 X IABC 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 V+ - OTA RIN 2RO ein gm ein 6 IOUT = gm (±ein) 2RO 3 + gm = 19.2 • IABC (mS) (mA) 4 V- RO ≈ 7.5/IABC (MΩ) (mA) ±IOUT ≈ IABC Max (mA) (mA) 5 IABC 1.0 NORMALIZED OUTPUT CURRENT AND DEVIATION FROM STRAIGHT LINE [ /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 () An IC Operational Transconductance Amplifier (OTA) With Power Capability CT SOLETE PRODU DIFFERENTIAL AMPLIFIER TRANSFER CHARACTERISTIC 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 FIGURE 3. THE OUTPUT CURRENT TRANSFER CHARACTERISTIC OF THE OTA IS THE SAME AS THAT OF AN IDEALIZED DIFFERENTIAL AMPLIFIER 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 1-888-INTERSIL or 321-724-7143 | Copyright © Intersil Corporation 2000 Application Note 6077 +6V VX SIGNAL INPUT 7 51 51 2 OTA CA3080A 3 + 6 IO 7 DIODE CURRENT = 0mA 6 5 100 4 IABC CA3080A S/N RATIO 500µA 80 3 60 10µA 2 S/N RATIO (dB) 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. 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. THD (PERCENT) 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. 40 1 20 THD 0 0.1 IO = gm VX AMPLITUDE MODULATED OUTPUT 0 1.0 10 100 1.0V INPUT VOLTAGE (mV) FIGURE 5A. 7 DIODE CURRENT = 0.5mA 10K 6 4 5 GAIN CONTROL 100 IABC CA3080A S/N RATIO 500µA 4 3 60 10µA 2 FIGURE 4. BASIC CONFIGURATION OF THE OTA DC GAIN CONTROL CIRCUIT 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 40 THD 1 20 0 0 1 10 100 1V 10V INPUT VOLTAGE (mV) FIGURE 5B. 7 DIODE CURRENT = 1mA 6 5 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. 80 S/N RATIO (dB) RM 5 100 4 80 500µA 60 3 2 1 IABC CA3080A S/N RATIO 10µA 40 S/N RATIO (dB) VM THD (PERCENT) -6V IABC THD 20 0 0 DISTORTION IS PRIMARILY A FUNCTION OF SIGNAL INPUT 1V 100 1 10 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 1 3 8 6 + 14 9 12 DIODE CURRENT 0.5mA 1mA 10K 7 11 100µA 10 6 3 5 2K EO CA3080A 4 0mA 10µA 2 GAIN EIN 1.0 DIODE CURRENT 13 0.1 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. CA3080 TRANSFER CHARACTERISTIC FOR THE CIRCUIT OF FIGURE 4 0 100 200 300 400 IABC (µA) 500 FIGURE 7. TOTAL SYSTEM GAIN vs AMPLIFIER BIAS CURRENT FOR SEVERAL VALUES OF DIODE CURRENT Horizontal: 0.5V/Div. Vertical: 50µA/Div., IABC = 100µA, Diode Current = 1mA FIGURE 9. CA3080 TRANSFER CHARACTERISTIC FOR THE CIRCUIT OF FIGURE 6 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 4-3 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. Application Note 6077 The CA3094 R2 R1 + DIFFERENTIAL INPUT R3 OUTPUT R1 R = 3 R2 R4 R4 R4 + - R5 R1 DIFFERENTIAL INPUT + R2 OUTPUT R1 = R3 R3 + R4 R6 R5 R7 = R6 R7 + - Implicit Tone Controls R1 DIFFERENTIAL INPUT R3 R2 R1 R2 = R4 R3 R4 + OUTPUT FIGURE 10. SOME TYPICAL DIFFERENTIAL TO SINGLE ENDED CONVERSION CIRCUITS +V IABC 500µA 5 2K 7 3 DIFFERENTIAL INPUT + 6 CA3080 2K 2 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 (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. - 4 OUTPUT RL 10K V- A = gm RL at 500µA, IABC: gm ≈ 10mS. ∴ A = 10mS x 10K = 100. FIGURE 11. A DIFFERENTIAL TO SINGLE ENDED CONVERSION CIRCUIT WITHOUT PRECISION RESISTORS 4-4 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. 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. Application Note 6077 ESIG = 40mV ESIG = 4mV ESIG = 4mV EO = 4V ATOTAL = 60dB EQUALIZER AREF = 32dB EN AT INPUT = 1 x 10-6 PICKUP ESIG =1mV 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 EO 4 POWER AMP 8Ω SPEAKER EN = 6.23 x 10-3 = 640 AT MAX VOL 6.23 x 10-3 EN EN = 4mV AT MIN VOL TOTAL GAIN = 72dB = FIGURE 12. BLOCK DIAGRAM OF A SYSTEM USING A “LOSSER” TYPE TONE CONTROL CIRCUIT ESIG = 40mV EO = 4V ESIG = 40mV ATOTAL = 60dB EQUALIZER AREF = 32dB EN AT INPUT = 1 x 10-6 PICKUP ESIG =1mV AMPLIFIER WITH FEEDBACK TONE CONTROLS EN = 5 x 10-6 VOLUME CONTROLS EN = 40 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. 4-5 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 8.2Ω 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 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 ) ------------- = – ---------------------------------2β 2βR 6 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 “BOOST” R20 (CW) 15K 0.12µF R9 68Ω C7 R7 “CUT” (CCW) 0.01µF 820Ω T1 + C9 220Ω 1W 0.001µF + 220Ω 1W 0.001µF - 5µF + D3 Q1 2N6292 30Ω C1 7 - D4 R11 330Ω Q2 2N6107 8 + 3 0.47Ω 27Ω CA3094 4700 µF Q3 2N6292 1 2 + 0.47Ω 3pF ES R1 120V AC D2 C3 15µF 5600Ω 120V AC TO 26.8VCT AT 1A D1 4700µF - R8 TREBLE 1800Ω C8 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 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 0.01µF 1.8K + + R5 1K + C10 1Ω 47Ω 0.47µF 3pF 47K FIGURE 15. A POWER AMPLIFIER OPERATED FROM A SINGLE SUPPLY 4-6 Application Note 6077 Performance 60 TREBLE BOOST BASS BOOST 55 50 EO /ES (dB) 45 FLAT 1.8 1.6 1.4 1.2 1.0 60Hz 0.8 60Hz 0.6 2kHz 7kHz 60Hz 12kHz 2 4 0.4 0.2 0 40 6 8 10 12 14 OUTPUT POWER (W) 35 30 FIGURE 18. IM DISTORTION OF THE AMPLIFIER WITH AN UNREGULATED SUPPLY 25 TREBLE CUT 20 Companion RlAA Preamplifier BASS CUT 15 10 2 10 3 68 2 100 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 1.0 26kHz 1kHz 0.9 2kHz 16kHz 0.8 0.7 0.6 4kHz TOTAL HARMONIC DISTORTION (%) INTERMODULATION DISTORTION (%) 2.0 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. 0.5 0.4 0.3 26kHz 0.2 16kHz 1kHz 0.1 4kHz 0 2 4 6 8 10 12 OUTPUT POWER (W) FIGURE 17. TOTAL HARMONIC DISTORTION OF THE AMPLIFIER WITH AN UNREGULATED POWER SUPPLY 4-7 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. 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 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). Application Note 6077 The derivative of Equation A1 with respect to I yields the incremental impedance of the Vbe multiplier: 120K V+ 5.6K R1 dE 1 K3 R2 BR 1 ---------- = Z = ------------- + 1 + -------------------------------------------------dI β+1 ( β + 1 )R 2 R 2 I e + K 3 0.002µF 680pF 1.5M 6 CA3080 1µF EOUT + 3 ES 50µF - - 2 5µF + 7 3.9K (EQ. A3) 4 where K3 is a constant of the transistor Q1 and can be found from: V be = K 3 lnI e – K 2 56K (EQ. A4) 5 56K Equation A4 is but another form of the diode equation: 5.6K V- 120K Ie = IS e 0.002µF 680pF 1.5M 7 3.9K + 2 - 3 + 5µF 1µF 6 CA3080 ES EOUT 4 qV be --------------- – 1 KT (EQ. 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. 56K 5 - Appendix B - Tone Controls 50µF 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: + 56K 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 + ------------------------β+1 R (β + 1) (EQ. A1) R1 + R2 + R3 Bass Cut: A LOW = ----------------------------------R2 + R3 C1 + C4 Treble Boost: A LOW = --------------------C4 2 C1 + C4 Treble Cut: A LOW = --------------------C4 E1 The asymptotic high-frequency gain is obtained by letting S increase without limit in each expression: R1 I R1 + R2 + R3 Bass Boost: A LOW = ----------------------------------R2 Vbe R1 + R2 Bass Boost: A HIGH = --------------------R2 R2 Ie R1 + R2 Bass Cut: A HIGH = --------------------R2 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 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 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 C2 C1 R2 R1 R3 R1 + R2 EO R3 - EO + ES ES ( R2 R3 + R1 R3 ) 1 + SC 2 -----------------------------------------( R1 + R2 + R3 ) R 1 + R 2 + R 3 A = ----------------------------------- ---------------------------------------------------------------+ R R R2 R3 2 3 1 + SC2 --------------------- R 2 + R 3 ( 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 R1 + R2 + R3 A LOW FREQUENCY = ----------------------------------R2 + R3 FIGURE B1 (A). BASS BOOST FIGURE B1 (B). BASS CUT C3 C2 C1 C4 C4 - REFF + C1 REFF EO - + EO ES ES ( 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 + 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 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 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. R2 CW R3 To make the controls work symmetrically, the low and high frequency break points must be equal for both boost and cut. CCW R1 C2 C1 Thus: - C1 R3 ( R1 + R2 ) C2 R2 R3 Bass Control: ------------------------------------------ = ----------------------R1 + R2 + R3 R2 + R3 + C2 R3 ( R1 + R2 ) and C 1 R = -----------------------------------------3 R1 + R2 + R3 FIGURE B2 (A). BASS CONTROL since R3 ≅ R2 + R3, C2 = 10C1 ( C1 C4 + C3 C4 + C1 C3 ) Treble Control: R 1 --------------------------------------------------------------C +C 1 C1 4 R1 CW C4 CCW R2 R1 R2 = --------------------- ( C 1 + C 2 ) R1 + R2 R R (C C + C C + C C ) ( C1 + C4 ) R 1 + R 2 C3 1 2 1 4 2 4 1 2 and R 2 C 3 = -------------------- --------------------------------------------------------------- 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 = ------------------------- FIGURE B2 (B). TREBLE CONTROL 2π × 1000 1 and for the treble control R 1 C 3 = ------------------------- 2π × 1000 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. 15K 0.001µF 1K 45 40 Q = 1.0 ES 820Ω - + EO 0.02 µF Q P = 1.0 35 Q = 0.99 30 0.2 µF 0.01µF 0.001 µF 1.8K P EO/ES (dB) 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. 68Ω 0.12µF 100K Q = 0.98 10K P = 0.99 P = 0.98 P = 0.96 Q = 0.96 25 Q =0.914 20 Q = 0.85 15 10 5 Q=0 0 10 100 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 P=0 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 4-10 Application Note 6077 45 40 40 35 35 30 GAIN (dB) GAIN (dB) 30 25 20 1000Hz 100Hz 15 1kHz 20 15 10kHz 31.6kHz 10 31.6Hz 10 25 5 5 0 0 0.2 0.4 0.6 0.8 1.0 ELECTRICAL ROTATION OF BASS CONTROL FIGURE B4 (A). 0.2 0.4 0.6 0.8 1.0 ELECTRICAL ROTATION OF TREBLE CONTROL 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. 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 4-11