APPLICATION BULLETIN ® Mailing Address: PO Box 11400 • Tucson, AZ 85734 • Street Address: 6730 S. Tucson Blvd. • Tucson, AZ 85706 Tel: (602) 746-1111 • Twx: 910-952-111 • Telex: 066-6491 • FAX (602) 889-1510 • Immediate Product Info: (800) 548-6132 AUTOMATIC GAIN CONTROL (AGC) USING THE DIAMOND TRANSISTOR OPA660 By Christian Henn, Burr-Brown International GmbH Multiplication of analog signals has long been one of the most important nonlinear functions of analog circuit technology. Many signal sources, however, such as CCD sensors, pin diodes, or antennas, deliver weak, oscillating, and simultaneously wide-band signals. But now a new multiplication method is available. Used as a wide-bandwidth Automatic Gain Control (AGC) application circuit, the integrated circuit OPA660 varies its own gain to change the signal amplitude and keep the output signal constant over a wide input voltage range. The OPA660 thus makes it possible to control and amplify signals with no additional multiplier. Important parameters include the differential gain (DG), the thermally induced pulse distortion, and the signal-to-noise ratio (S/N). An analog multiplier delivers an output signal (voltage or current) that is proportional to the product of two or more inputs. The application circuit presented here is concerned primarily with two inputs. In the simplest case, each of the two inputs can function with both polarities. In this case, the input voltage swing covers all four quadrants; that is, there are four polarity combinations. In contrast to a four quadrant multiplier, a two quadrant multiplier allows only one input to be connected to a signal of any polarity. The second input can only process unipolar signals. quiescent current programmer, it can also be used for multiplicative applications. Figure 1 illustrates the dependance of the transconductance (gm = d(IOUT)/d(VIN)) upon the resistance, RQC. The following equation can be derived from the idealized OPA660 model circuits shown in Figure 2. V IQC = T ln (n) RQC When the temperature voltage (VT) is 25.86mV, the quiescent current resistance (RQC) is 250Ω, and the scale factor (n) of the transistor R122 is 10, the cross current IQC can be calculated as follows: IQC = 25.86mV ln(10) = 238µA 250Ω The quiescent current of the subsequent transistor stages can be calculated with a scale factor (a) of 7.3 for transistors 31, 32, 81, and 82 to IQC' = a • IQC = 7.3 • 238µA = 1.74mA IOUT (mA) Multipliers are nonlinear and thus can not be implemented as simply and exactly as linear components. In developing the circuit, various design methods were used depending upon the accuracy, bandwidth, and justifiable complexity. Multipliers do have several disadvantages, including linearity errors, temperature dependence, less than ideal crosstalk, and limited bandwidth, but the multiplication function presented here functions directly and has variable transconductance, enabling it to achieve the largest possible bandwidth. RQC 1.5 250 1.0 500 0.5 –20 –15 –10 10 15 20 VIN (mV) –0.5 –1.0 AGC WITH THE DIAMOND TRANSISTOR The voltage-controlled current source of the OPA660 from Burr-Brown has acquired various nicknames according to its applications: –1.5 VOUT = VIN Operational Transconductance Amplifier (OTA) Current Conveyor Diamond Transistor Ideal Transistor Macrotransistor VIN 1993 Burr-Brown Corporation VOUT RQC Applications for the OPA660 are usually amplifier circuits. But although the OPA660’s connection pin, IQ, adjusts functions primarily as a power supply switch or © M M RQC FIGURE 1. Schematic Diagram of the Multiplication Function. AB-185 Printed in U.S.A. October, 1993 BC 7 (13) DB 7 (13) DT 7 (13) IQC' 7.3(x) IQC' IQC 81 IQC IQC Rgm IQC 31 8 6 5 IQC' 7.3(x) 2 3 7.3(x) 32 82 10(x) (14) 122 IQC' IQC (14) IQC' IQC 7.3(x) (14) IQC' 4 4 4 RQC 250Ω FIGURE 2. Idealized Model Circuit. Now it is easy to determine the transconductance using the following equation: gm = IQC VT = gm, since it is dependent upon the modulation. This change results in turn in signal distortion. The following equations derive the relation between the signal amplitude and distortion. a • ln(n) = 67mA/V RQC VOUT = i • ROUT = VIN • gm • ROUT = VIN • i = I1 – I2 = IQC' Exp + M RQC ϕ= VIN – Rgm • i VIN + 2IQC' Rgm • sinh (ϕ) ∆V = = 2VT 2VT VT VIN = 2VT • ϕ –2IQC' Rgm • sinh (ϕ) a • ln(n) • ROUT d(i) = –2IQC' • cosh (ϕ) d(ϕ) RQC = ±10mV 7.3 • ln(10) • 2.08kΩ 250Ω ∆V VT ( ) – Exp – i = –IQC' [Exp (–ϕ) – Exp (+ϕ)] = –2IQC' • sinh (ϕ) When the resistor (ROUT) has 2.08kΩ and the input voltage is ±10mV, the output voltage reaches the following value: VOUT = ∆V VT ( ) The circuit diagram of the actual multiplier circuit as illustrated in Figure 3 makes it easier to determine the multiplication constant, M. The signal current at Pin 8 produces the following output voltage at the resistor ROUT: = ±1.4V d(VIN) d(ϕ) = –2VT –2IQC' Rgm • cosh (ϕ) The multiplication constant M can be derived directly from the equation as follows: cosh (ϕ) = sinh2 (ϕ) + 1 = M = a • ln(n) • ROUT = 7.3 • ln(10) • 2.08kΩ = 35kΩ ( ) i/IQC' 2 2 +1 The gain G can be calculated using the equation: G= d(VOUT) d(VIN) = M 35kΩ = = 140 RQC 250Ω gm = DETERMINING THE DIFFERENTIAL GAIN (DG) d(i) d(VIN) = VT Rgm + IQC' 2 d(VIN)/d(ϕ) ( ) i/IQC' 2 1 = 1 = Figure 4 shows the circuit part important for the multiplication. When VIN = 0, i = 0, and I1 = I2 = IQC’, i increases with rising VIN, resulting in variation of the currents I1 and I2. The increase in both currents also changes the transconductance d(i)/d(ϕ) 2 +1 Rgm – VT IQC' cosh (ϕ) IQC' = gm0 = DG = gmMAX The following applies for low modulation: a • ln(n) •VT iMAX ≈ RQC 1 or for low modulation: –1= VT/IQC' Rgm + ( 2 +1 a • ln(n) Rgm/ (RQC + 1) a ln(n) Rgm/RQC + VIN/VT 2 (a • ln(n) Rgm/ (RQC + 1) 2 +1 8 5 VIN ±10mVp0 –1 1 VOUT ±1.4Vp0 i +1 2 (Rgm +VT/IQC') ROUT 2.08kΩ 7 2 VIN/IQC' 2 ≈ +5V VT/IQC' Rgm + ) iMAX/IQC' Rgm + VT/IQC' DG ≈ Rgm + VT/IQC' gm0 Rgm + VT/IQC' In the extreme case in which Rgm = 0, the following results: i=0 Rgm + VT/IQC' VINMAX 3 DB OPA660 DT 4 6 Rgm 1mΩ 2 DG0 = ( iMAX/IQC' DG0 ≈ ( VINMAX 2 ) +1 – 1 ) +1 – 1 1 RQC 250Ω 2VT 2 Figures 5 through 8 show an analysis of the equation DG = f (VIN; Rgm; RQC), which determines the differential gain error dependent upon the input voltage. The figures include the open-loop gain resistance (Rgm) and quiescent current resistance (RQC). –5V FIGURE 3. Multiplier Circuit. As is evident, Rgm produces transfer linearization, but it also reduces the gain, GRgm. IQC' VIN IQC' ∆V I1 i Rgm I2 i I2 GRgm = d(VOUT) d(VIN) ∆V Rgm + IQC' ROUT Rgm +VT/IQC' ROUT = I1 = RQC i=0 a • ln(n) IQC' As will be shown later, the gain reduction results in a poorer signal-to-noise ratio (S/N). Designers can determine the best performance compromise for DG and S/N by choosing appropriate values for VINMAX and Rgm. However, the larger the control range —that is, the greater the variation of RQC —the poorer the quality of the compromise that can be attained. FIGURE 4. Multiplier Section. 3 10 0 DG max RQC = 250Ω 3 0 RQC = 500Ω 10 3 20 1 (%) Rgm (Ω) (%) 10 1 30 40 20 0.3 50 0.3 30 Rgm (Ω) DG max 10 40 0.1 0.1 –20 –10 0 10 –20 20 –10 10 0 VIN (mVpo) FIGURE 5. Differential Gain Error (RQC = 250Ω). FIGURE 6. Differential Gain Error (RQC = 500Ω). 10 10 3 20 1 30 40 50 (%) RQC = 1kΩ 0.3 0 10 20 30 40 50 RQC = 2kΩ 3 Rgm (Ω) DG max 0 Rgm (Ω) DG max 10 (%) 20 VIN (mVpo) 1 0.3 0.1 0.1 –20 –10 0 10 20 –20 –10 10 0 VIN (mVpo) 20 VIN (mVpo) FIGURE 8. Differential Gain Error (RQC = 2kΩ). FIGURE 7. Differential Gain Error (RQC = 1kΩ). When Rgm is inserted, the relation between the gain, GRgm, and the control value, 1/RQC, becomes disproportionate. Reference for VOUT – + AUTOMATIC GAIN CONTROL (AGC) Circuit tolerances and insufficient temperature compensation result in undefined gains (GRgm = f(RQC)) of about ±25%. If RQC is implemented by a FET, this undefined gain range increases even more. These problems can be avoided by using an AGC circuit as shown in Figure 9. Automatic Gain Control VIN VOUT Multiplier Amplifier Level Control In the detailed circuit in Figure 10, the ±0.7V input signal (VIN), which is assumed for now as a constant, is divided by the input divider (4kΩ/56Ω) to about ±10mV. The 4kΩ resistor in front of the circuit can, of course, be removed if the input amplitude is only in the mV range, as is the case in fiber optic transmission receivers. The amplifier (OPA621) placed after the circuit converts the output current i of the multiplier (OPA660) into voltage. The peak detector and comparator compare the ±1.4V output signal (VOUT) with the given reference value +1.4V and connect the control voltage to the FET. This control ensures that the peak value of VOUT is identical to the adjustable reference DC voltage and is FIGURE 9. AGC Circuit (Schematic). unaffected by circuit tolerances. It is also possible to control the output voltage against the black level or synchronization level by acquiring the output voltage for comparison only during the horizontal sync time. While the luminance signal changes over time, the sync level is always transmitted with constant amplitude. Such regulation enables the video signal to be transmitted at a constant amplitude despite changes in the luminance signal. 4 VOUT ±1.4Vp-p +5V 3 2 7 OPA621 6 4 ROUT 2.08kΩ –5V +5V i ±10mVp-p 8 7 +5V OPA660 4kΩ VIN 5 DB 10kΩ 22kΩ 3 DT 56Ω Offset –5V 56Ω 6 4 ±0.7Vp-p –5V Rgm 1mΩ 2 1 RQC 250Ω Peak Detector and Comparator 1.4V +5V –5V –5V Reference for VOUT FIGURE 10. AGC Amplifier for Various Signals. +5V To Multiplier Pin 1 +5V 100kΩ 2.7kΩ 0.47µF +1.6V Reference for VOUT +0.4V 0.47µF 100Ω 100Ω 1kΩ 330Ω 2811 RQC 2* BC577 2N5460 2.2MΩ VOUT ±1.4Vp-p 2811 2.2MΩ + 0.47µF 1MΩ –5V FIGURE 11. Peak Level. To Multiplier Pin 1 +5V Variations in the input signal amplitude cause the control system to produce constant output signal amplitudes corresponding to the reference value. Simultaneous changes in VIN and the reference value are also possible. VOUT 3 7 CA3080 6 ∞ 2 5 4 10kΩ DETERMINING THE MAXIMUM DIFFERENTIAL GAIN (DGMAX) OF AGC AMPLIFIERS –5V Hk 47kΩ 0.1µF 2N3904 The input voltage of AGC amplifiers varies from VINMIN to VINMAX. To maintain a constant output voltage (VOUT) over this range, the control voltage from the peak level control varies the resistance RQC correspondingly from RQCMIN to R QCMAX. The largest signal distortions measured as 4Vp-p 1N4148 –5V FIGURE 12. Clamp Circuit for TV Signals. 5 C hold 1µF differential gain (DGMAX) happen at VINMAX or RQCMAX, thus during operation of the OPA660 with the smallest quiescent current IQ. For the control range q of the AGC amplifier, the following conditions apply: q= It should be kept in mind, however, that this equation is based upon the simplified model shown in Figure 2 and sometimes deviates from measurements and simulation results. The measurements, for example, also include distortion from the subsequent amplifier OPA621. Figures 13 to 15 give an overview of the achievable distortion. For maximum input voltages (VINMAX) from ±10mV to ±20mV and open-loop resistances from 0Ω to 50Ω, the differential gain shown in simulations is a function of the ratio VINMAX/VINMIN and equals 9. Figure 16 presents measured achievable distortions in the AGC structure, as already shown in Figure 10. VINMAX VINMIN RQCMAX = q • RQCMIN + a • ln(n) • Rgm • (q – 1) B = a • ln(n) • Rgm/RQCMAX THERMALLY INDUCED DISTORTION As shown in Figure 2, the power consumption of transistors 31, 32, 81, and 82 varies according to the signal curve. This variation leads to temperature oscillation and finally to change in the transconductance gm. From these equations, it is possible to derive the maximum distortion, DGMAX, as a function of B and the maximum input voltage. At first glance, it looks as if the pulse distortion is caused by RC parts. The visible thermal time constant, however, is in the microsecond range and is negatively affected by unequal temperature distribution on the chip. B+1 DGMAX = 1 B+ 2 VINMAX/VT +1 2 (B + 1) As Figure 17 shows, Rgm can reduce this thermally induced pulse distortion. 10 DGMAX DGMAX VINMAX = 10mVp0 1.0 (%) 0 10 20 30 40 50 0.3 1.0 0.3 VINMAX/VINMIN VINMAX/VINMIN 0.1 0.1 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 FIGURE 14. DGMAX of the AGC Amplifier (Simulation) (VINMAX = ±15mV). FIGURE 13. DGMAX of the AGC Amplifier (Simulation) (VINMAX = ±10mV). 10 3.0 1.0 DGMAX VINMAX = 20mVp0 0 10 20 30 40 50 3.0 (%) VINMAX = 20mVp0 Rgm (Ω) DGMAX 0 10 20 30 40 50 0.3 1.0 Rgm (Ω) 10 (%) 0 10 20 30 40 50 3.0 Rgm (Ω) (%) 3.0 VINMAX = 15mVp0 Rgm (Ω) 10 0.3 VINMAX/VINMIN VINMAX/VINMIN 0.1 0.1 1 2 3 4 5 6 7 8 1 FIGURE 15. DGMAX of the AGC Amplifier (Simulation) (VINMAX = ±20mV). 2 3 4 5 6 7 8 FIGURE 16. DGMAX of the AGC Amplifier (Measurement) (VINMAX = ±20mV). 6 In contrast, periodic RF signals less than 1MHz are barely affected by the pulse distortion. The temperature change can no longer follow the signal change, resulting in more balanced temperature distribution on the chip. 10 8 VINMAX = 20mVp0 DGMAX 0 6 20 (%) DEMO BOARD All available measurements were conducted using the completely dimensioned circuit shown in Figure 19. The demo board designed for this application contains four circuit blocks. As a differential amplifier with current output, the OPA660 allows users to control the transconductance by varying the total quiescent current. Functioning mainly as a multiplier, it also enables a shift in DC position of the output voltage by varying the noninverting OPA660 input. The OPA621 functions as a current-to-voltage converter and amplifies the signal. The switch, S1, in the shift block lets the user choose between manual, and automatic offset compensation, and clamped DC restoration. At active LOW, the clamp pulse triggers the OTA module CA3080, checks the output voltage (VOUT) against the reference value for the black level voltage, and stores the correction voltage up to the next clamp pulse (HK) in the capacitor CHOLD. The fourth block is the already mentioned peak level control circuit. The discrete differential amplifier checks the peak value of the output voltage (VOUT) against the reference voltage set by PREF. The transistor 2N5460 changes the quiescent current according to the difference, thus varying the transconductance gm. 30 40 50 2 Rgm (Ω) 10 4 VINMAX/VINMIN 1 1 2 3 4 5 6 7 8 FIGURE 17. Effect of Rgm on Thermal Pulse Distortion. 64 VINMAX = 20mVp0 60 52 48 44 VINMAX/VINMIN 40 1 For applications requiring frequencies of more than 80MHz and a controlled output voltage (VOUT) of more than ±1V, we recommend two-stage gain using two OPA621s. With the amplifiers OPA622 and OPA623, it will be possible to increase the bandwidth even more. 2 3 4 FIGURE 18. S/N of AGC Amplifiers. 7 5 6 7 8 0 10 20 30 40 50 Rgm (Ω) S/N (dB) 56 +5V Amplfier R6 100Ω 10nF 2.2µF 9 OPA621 2 R7 VOUT 20kΩ 4 2.2µF 10nF 0.2 ... 0.8Vp-p VOUT 2.8Vp-p 7 3 –5V +5V Level-Shifting POFFSET +5V 2.2µF i VIN DB 10nF 3 DT 7 CA3080 4 R8 10kΩ +5V R3 56Ω OPA660 R1 56Ω C5 +470µF 3 4 Clamped 8 – Automatic S1 5 R4 22kΩ R5 56Ω ±13mV 2 1 10nF RIN 2kΩ –5V Manual 7 6 R2 51Ω 10nF 2 3 CHOLD C4 R 20 1µF 10Ω 2 5 2.2µF R11 1kΩ 6 1 Rgm 2.2µF R22 1kΩ 10nF 2.2µF –5V 0.1µF Multiplier R9 51Ω R21 47kΩ R23 560kΩ –5V C6 0.1µF 4Vp-p –5V +5V +5V Peak Level-Control 220µF PREF VREF 1kΩ +0.4V R17 330Ω R10 R18 100kΩ R16 2.7kΩ +1.6V D1 HK 2N3904 –5V – C2 + 0.47µF 2811 RQC R14 2.2MΩ R13 100Ω R15 100Ω – C 3 + 0.47µF 2* BC577 2N5460 + – C1 4.7µF D2 2811 R12 2.2MΩ R19 1MΩ 220µF –5V FIGURE 19. Circuit Diagram of the AGC Amplifier Demo Board. 8 FIGURE 20. Layout of the AGC Amplifier Circuit Board — Back. FIGURE 21. Layout of the AGC Amplifier Circuit Board — Front. 9 PARTS LIST NUMBER OF PARTS NO. DESIGNATION PART NAME/VALUE 1 IC1 OPA621KP 1 2 IC2 CA3080 1 3 IC3 OPA660AP 1 4 T1, T2 BC577 2 5 T3 2N5460 1 6 T4 2N3904 1 7 D1 , D2 2N2811 2 8 D3 IN4148 1 9 R1, R3, R5 56Ω 3 10 RIN 2kΩ 1 11 Rgm 51Ω 1 12 R6, R13, R15 100Ω 3 13 R7 20kΩ 1 14 R4 22kΩ 1 15 R8, R20 10kΩ 2 16 R11, R22 1kΩ 2 17 R23 560kΩ 1 47kΩ 1 2 18 R21 19 R10 20 R12, R14 2.2MΩ 21 R18 100kΩ 1 22 R17 330Ω 1 23 R16 2.7kΩ 1 24 R19 1MΩ 1 1 25 Capacitor 2.2µF 6 26 Capacitor 10nF 6 Capacitor 220µF 2 28 27 C2 , C3 Capacitor 0.47µF 2 29 C5 Capacitor 470µF 1 30 C6 Capacitor 0.1µF 1 31 C4 Capacitor 1µF 1 32 PREF POT 1kΩ 1 33 POFFSET POT 10kΩ 1 34 VIN, VOUT, HK SMA 3 35 POS, GND, NEG Mini-Banana 3 10

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