ECE2280 Homework #1 Fall 2011 1. Use: ignore r o, V BE =0.7, β=100 V I = 200.001sin(20t) For DC analysis, assume that the capacitors are open (a) Solve for the DC currents: a. I B b. I E c. I C (b) Solve for the DC voltages: a. V B b. V E c. V o V I 1m Vx 0-1mA C3 100m I1 4kΩ 4kΩ 2k 16V I B 6kΩ 10k I C V o V Q1 B 2V I E 8V 10V 100Ω C4 100m Q2N3904 V E 6.7V 900 100Ω 100 1k (c) Prove or disprove the region of operation you assumed to solve for your answers in (a) and (b)? 4kΩ 6V R out 1
2. Use: ignore r o, V BE =0.7, β=100 V I = 50.001sin(500t) r π1 =2, 000 g m2 =50mA/V, and I B2 =12.5µA V sig For the following hybrid-π equivalent circuit below, find the following values: (a) R in (input resistance ignore only the input source, Vsig and include all resistors at the base) (b) R out (output resistance-include all resistors at the collector{no load is connected}) Vo (c) midband gain, Vsig 2k 3kΩ 2kΩ ~ Rin 100Ω 2kΩ V π1 - r π1 g m1 V π1 V π2 - r π2 g m2 V π2 6kΩ Vo 1kΩ 4kΩ 4kΩ 3kΩ R out 2
3. For the circuit shown below, draw the AC small-signal equivalent circuit(use hybrid-π or model T). Make sure that everything is labeled in terms of the transistor number. (e.g. g m1, v π2, etc.). Include r o for all transistors. v sig =0.001sin(10t) AC. Assume all capacitors are shorted. 15V R 4 v sig R 6-15V 3
4. Use: V t =2V k n (W/L)=4mA/V 2 λ=0 V I = 100.002sin(20t) For DC analysis, assume that the capacitors act as open (d) Solve for the DC currents: a. I 1 b. I D c. I S (e) Solve for the DC voltages: a. V G b. V S c. V o (f) Verify that the transistor is saturated. (g) State the DC bias point. ~ C 3 1m V I (h) Assuming that the transistor amplification Vo/V I = -7V/V. What is the total (AC and DC) instantaneous output for Vo (V I value stated above). R in 2k 2k 4V V G I 1 I S I D V o 9V 3k NMOS V S 500Ω 1.7V 500Ω C 4 100m R out 1k 4
5. Use: V t =2V k n (W/L)=3mA/V 2 V sig is an AC source Transistor 1 has DC values: V GS =4V, I D =6mA Transistor 2 has DC values: V GS =5.3V, I D =16.7mA λ=0 (for all transistors) For the following hybrid-π equivalent circuit, find the following values: (a) R in (input resistance ignore the input source, Vsig) (b) R out (output resistance-ignore R L {no load is connected}) Vo (c) midband gain, Vsig 3MΩ 2kΩ v sig ~ v 2MΩ gs1 1kΩ gm1v gs1 1kΩ v gs2 gm2v gs2 V o R in 1kΩ R L = 1kΩ R out 5
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6. For the circuit shown below, draw the AC small-signal equivalent circuit(use hybrid-π or model T). Make sure that everything is labeled in terms of the transistor number. (e.g. g m1, v gs2, etc.). λ=0 for all transistors. v sig =0.005sin(20t) AC. Assume all capacitors are closed for the AC circuit. 15V 10V R 3 1mA R 8 V sig ~ C 3 100m R1 R 6 R 2 1V NMOS M 1 R 7 NMOS M 2 R 9 R 4 5V R 10 C 1 10m R 5-15V 7
7 (a) Design the cascode amplifier with 2 PMOS transistors for the current source(as shown in class or Fig. 7.11) at a current of 0.1mA with all devices operating at Vov =0.25V. All devices have V A =4V. Find g m1, the output resistance of the amplifier, Ron, the output resistance of the current source, Rop, the overall output resistance, Rout, and the voltage gain, Av. (b) Use the same circuit with the following DC voltages: V In =0.8V, V G2 =1.2V, V G3 =1.3V, V G4 =1.7V, and V DD =2.5V. If all devices are matched, that is k n1 = k n2 = k p3 = k p4, and have equal V t =0.5V, what is the overdrive voltage at which the four transistors are operating(note this is different from part (a))? What is the allowable voltage range at the output? (a) (b) 8
8. Design the cascode amplifier that utilizes 2 PMOS transistors for the current source to have the following specifications: g m1 =2mA/V, and Av=-200V/V. Assume that the available fabrication process has V A=5V/µm for both NMOS and PMOS devices and that µ n C ox = 4µ p C ox =400µA/V 2. Use the same channel length L for all devices and operate all four devices at Vov =0.2V. Determine the required channel length L, the bias current I, and the W/L ratio for each of four transistors. Assume that suitable bias voltages have been chosen, and neglect the Early effect in determining the W/L ratios. 9
9. A cascode current source formed of two pnp transistors for which β=50 and VA=5V supplies a current of 0.5mA. What is the output resistance? 10. The figures below show four possible realizations of the folded cascode amplifier. Assume that the BJTs have β=100 and that both the BJTs and the MOSFETs have V A =5V. Let I=100µA, and assume that the MOSFETs are operating at V OV =0.2V. Assume the current sources are ideal. For each circuit determine, Rin, Rout, and the gain Vo/V I. Comment on your results. (a) 10
(b) (c) (d) 11