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ECE 3183 Problems in ideal Opamps Version 3.7 OA-1: Assuming ideal opamps, determine the voltage transfer gain T = vO/vS and input resistance Rin for each of the configurations shown. Resistances are in kΩ. 100 200 25 25 vS vO vO vS 40 25 125 25 25 vO vS vS 10 vO 40 10 OA-2: (a) Using resistances no larger than 10 MΩ design an amplifier with gain -50 V/V, using the inverting configuration. Assume ideal opamp. (b) What is the input resistance (c) What is the feedback ratio β? R2 R1 vS vO Answers : (a) 200 kΩ, 10MΩ (b)100 kΩ, (c) 1/51 OA-3: Find (a) transfer function T = vO/vS and (b) input resistance Rin. Resistances are in kΩ 200 200 50 50 Answers ((a) -24 V/V, (b) 50 kΩ OA-4: vS vO Find (a) transfer function T = vO/vS and (b) input resistance Rin 200 200 200 200 200 50 vS 200 200 200 100 vO vS vO OA-5: Find (a) transfer function T = vO/vS and (b) input resistance Rin 200 200 100 200 100 100 200 100 100 200 200 100 vO vS vO vS Answers: (a) 8 V/V, (b) 16 V/V OA-6: Find transfer function T = vO/vS vO vS 100 100 100 OA-7: Design a 4-bit digital-analog converter using the R2R ladder as shown such that Vo = 4.0V when the input word = $C = %1100. Assume input levels of 2.0V and 0.0 V, respectively. V0 V1 2R V2 2R 50 50 50 V3 2R 2R vO And assume R1 = R = 10 kΩ 2R R R R 2R R2 R1 OA-8: A sinusoidal input with phase shift = 0 is fed to a Miller integrator that uses an ideal opamp and an RC pair with R = 50 kΩ and C =.001 µF. (a) At what frequency are the input and output signals equal in magnitude? (b) What is the phase of VO relative to Vin? (c) If the frequency is decreased by a factor of 10 from that of part (a), by how many dB does the output change? Answers: 3.2kHz, +90o, 20 dB OA-9: A lossy Miller integrator, as shown, uses an ideal opamp. A sinusoidal signal is applied to the input. (a) at what frequency are the input and output signals equal in magnitude? (b) What is the phase of vo relative to vin? (c) If the frequency is decreased by a factor of 10 from that of part (a), by how many dB does the output change? .002µF 500 vO vin 50 OA-10: (a) Show that the transfer function for the configuration shown is Cf R2 ⁄ R1 T = – -----------------------------------------------------( 1 + ω1 ⁄ s ) ( 1 + s ⁄ ω2 ) C1 Rf vO vS where ω1 = 1/R1C1 and ω2 = 1/RfCf R1 The circuit has the frequency response of a bandpass for which the low-frequency roll-off is at ω1 and the high-frequency roll-off is at ω2 (b) By choice of R1, R2, C1, C2, design a circuit such that Rin = 10 kΩ (ω1 << ω < ω2), midband gain = 46 dB, low-frequency rolloff corner = 200Hz and high-frequency rolloff corner is 40 kHz. OA-11: The circuit shown uses a 250kΩ potentiometer to implement an adjustable gain amplifier. vO vS (a) Assuming R1 = 20k, derive an expression for the gain as a function of parameter setting x. 1-x 100kΩ POT x (b) What value of R1 is necessary so the gain will range from T = 1.0 to T = 21 V/V? OA-12: A photodetector with source voltage 100 mV and source resistance 100 kΩ is connected to a 1 kΩ load. Find the voltage that will appear across the load if: R1 RSOURCE (a) vS RLOAD (a) it is connected directly to the load. (b) an ideal unity-gain buffer is inserted between the source and the load. RSOURCE (b) vS RLOAD OA-13: The circuit shown is called a level-shifting buffer. +10V 25kΩ (a) Determine the range over which the output level V can be adjusted. v x (b) Assume that a 20-turn potentiometer is used. Find the change of V with respect to each turn of the pot. vO = V + v 1-x 25kΩ -10V 200kΩ POT OA-14: Find transfer functions for each of the following circuits (A) R (B) 2C vO C vS vS R R/2 C R R C vO R (C) R R R’ = xR + R’ 0<x<1 vS vO - R R R OA-15: Find vo as a function of v1 and v2. Resistances in kΩ v1 Answer (a) vo = 10 (v2 - v1) (b) What is the transfer gain if R3 is changed to 100 kΩ? 10 20 25 vO R3 = 10 25 10 20 v2 OA-16: Design the variable-gain instrumentation amplifier shown such that it will realize a differential gain that is variable in the range 1 to 50 using a 100 kΩ potentiometer as a variable resistance. Suggestion: Design the second stage for a gain of 0.5. v1 R2 R1 R4 r vO Answers (a) R2/R1 = 0.5, r = 0.5kΩ, R4 = 50kΩ. R R4 R1 R2 v2 OA-17: Assuming ideal opamps determine the 3dB frequency for the following 4-stage circuit in terms of the time constant τ = RC. (Hint: Assume each stage loses 3/4 dB) R R R R vI vO C C 200 C C 200 200 100 200 50 200 200 100 100 vO vS vS vO 0.52µm 20nm 1µm 2µm