Analog Electronics

Problem 2: Consider the amplifier shown in Figure 2. Ignore CL. Assume that all transistors are in saturation. (a) Express the small signal transconductance of M3 namely gm3, in terms the small signal transconductance of M2, namely gm2. Hint: You can assume that VSD is the same for M2 and M3. (b) Determine the gain, Ay, of the amplifier. (3+7= 10 points) Bs M₂ W/L WHhM₁ R₂. Figure 2 M₂ 4W/L C₂₁

Suppose the BJT drawn has Ic = 1 mA when VBE = 0.6 V. (a) Draw the transfer function plot for Rin for the range 10 kΩ < Rin < 100 kΩ, assuming Rin < ZL for the entire range. (b) Assuming an ideal BJT, calculate the output impedance at the slave BJT's collector node. (c) Justify: what is the danger if Z₁ > Rin?

The circuit in Fig. 1(a) is a sensor readout circuit developed by MEMS/NEMS research group (simple but effective) at EE&T UNSW for amplifying a small charge (voltage) generated by a PZT thin film in a micro-lens actuator when the actuator resonates. A PZT stands for lead zirconium titanate. It is a piezoelectric material that transduces strain into an electrical charge (voltage) and conversely applied voltage (charge) into strain. Hence, the material is used to build actuators, which are devices that produce mechanical energy (force, moment and etc) from electrical energy (applied voltage) - the most precise nanoscale movements in advanced equipment, robotics, automobile, energy harvesters, and others are enabled by piezoelectric actuators. The same material is also used to build sensors to detect tiny movements, pressure, and forces such as touch screens, pressure sensors, accelerometers, gyroscopes and etc. Fig. 1(b) shows the sensor readout circuit with the PZT actuator replaced by its electrical equivalent circuit that consists of a voltage source (VPZT) in series with a capacitor (CPZT). When the actuator is excited (driven) by Vin, it resonates and generates small VPZT. Hence, VPZT is in phase with Vin

Problem 2: Consider the circuit shown in Figure 2. Assume that µnCox= 200μA/V², VDD=1.25V, VTH=0.5V, W/L=1, and Rò=10kQ. Ignore channel length modulation. (a) Determine the drain current, ID. (b) Draw the small signal model of the circuit. Show the component values. Consider channel length modulation, assume λ = 0.8V-¹. (c) Calculate the impedance looking into the terminal 1-1', using the small signal model in (b). (3+3+4=10 points) VDD SRD M₁ Figure 2

y(t)=4 \cos (2 \pi 200 t)+3 \cos (2 \pi 400 t)-2 \cos (2 \pi 800 t)-3 \cos (2 \pi 1400 t)+5 \cos (2 \pi 1600 t+\pi / 2) a) Find the DT signal obtained by sampling y(t) with a sampling period of T = 1 msec/sample.Express your answer in the simplest form possible and comment on aliasing. (Do NOT need to sketch the signal). b) Repeat part a) for a sampling rate of 3200 HZ ( t= 1/3200 SEC/SAMPLE) AND EXPLAIN WHY NYQUIST SAMPLING CONDITION IS Fs > 2Fmax rather than simply Fs = 2F max c) Repeat part a) for a sampling rate of 3300 Hz.

X_{c}(t)=2 \cdot \cos (2 \pi 40 t)+3 \cdot \sin (2 \pi 60 t)-\cos (2 \pi 160 t)-\cos (2 \pi 300 t)+4 \cdot \sin (2 \pi 340 t) is ideally sampled with = 2(pi)100 rad/sec. What is the output signal X„(t) which is obtained by passing the sampled signal through a reconstruction filter which is an ideal bandpass filter with cutoff frequencies N, = 2(pi)120 and (omega) = 2(pi)180 rad/sec and G=T ?Hint:

the message signal m(t) has the Fourier transform shown in Figure P-3.11(a). This signal is applied to the system shown in Figure P-3.11(b) to generate the signal y(t).The 1. Plot Y(f), the Fourier transform of y(t). 2. Show that if y(t) is transmitted, the receiver can pass it through a replica of the system shown in Figure P-3.11 (b) to obtain m(t) back. This means that this system can be used as a simple scrambler to enhance communication privacy.

A DSB-SC AM signal is modulated by the signal m(t)=2 \cos 2000 \pi t+\cos 6000 \pi t The modulated signal is u(t)=100 m(t) \cos 2 \pi f_{c} t where fe = 1 MHz. 1. Determine and sketch the spectrum of the AM signal. 2. Determine the average power in the frequency components.

For the IC current mirror, which uses matched components, shown in Figure Q2: Derive the equation for the finite current gain error: I out \ I ref Determine the output current for B= 40 and ß= 15,assuming +Vc =+15V , |VBe| = 0.7V, and R =14.3k Calculate the output impedance for the previous two output currents,assuming that the Early voltage of the integrated transistors is: V, = 100V.

An integrated differential amplifier circuit with component and power supply valuesis shown in Figure Q1. The amplifier uses matched IC components. i) Calculate all the quiescent transistor currents and voltages for transistors Q1 and Q2.Hint: ignore the dc voltage drop on resistors R3 and R4. ii) Using the currents evaluated in (i), determine the differential small-signal voltage gain in dB, the single input-output small-signal voltage gain in dB, and the differential input resistance Rin in k2 if ß = 400.%3D iii) Calculate the Common Mode Gain (CMG) and the Common Mode Rejection Ratio(CMRR) in dB. Assumptions:Quiescent means with zero input signal (with grounded inputs). Also, B>> 1 so you may ignore base currents. VBE = 0.7 V, VT = 26 mV.