1.(a) Comment the mechanism and the properties of the thermal noise [5 marks] (b)The amplifier circuit shown in Fig. 1 has an effective noise bandwidth of 5 MHz. Given that the differential amplifier has equivalent input noise current and voltage densities of 1 pA/√Hz and 1 nV/√Hz respectively. Sketch the noise equivalent circuit and hence determine values for: (i) The equivalent input noise current and voltage of the circuit (excluding the source); (ii) The output signal-to-noise (S/N) ratio, given a 1 V (rms) sinusoidal source (VS) and a 1 kΩ source resistance (RS); (iii) The noise figure (F) of the amplifier circuit; (iv) The optimal value of RS and determine minimal noise figure of the circuit. [20 marks] -20 Note: Assume that 4kT= 1.65 x 10 J. R2 10kΩ -

RS

+

1kΩ

VS

VO

100kΩ

R1

Fig. 1. 2.(a) The circuit of ramp generator is shown in the Fig.2. At the time instant t=0 the switch S is opened. Describe the performance of this circuit assuming the ideal components and E = +10 V. [12 marks] +E

D1

VP R

V1

C2

V2

R1

S C1

R2

Vo

Figure 2. (b) Determine the values of all appropriate components to produce output ramp: 5 V/ms . [6 marks] (c) Make appropriate changes in the circuit to produce a linear current ramp in an inductor, connected to the output. Assume that the inductor L (0.5 mH) has an associated series (winding) resistance r (5 Ω). Determine the value of the current ramp. [7 marks]

3(a) Describe two different approaches for signal shaping/transformation. State briefly the appropriate examples. [7 marks] (b) The circuit shown in Fig. 3a is to be used to generate the following piece-wise linear function: dVO/dVS = -1; -2 V ≤ VS ≤ +2V dVO/dVS =-2; |VS| ≥ 2V Assuming ideal components and that R1 = 10 kΩ, determine values for R2, R3, R4 and the d.c. reference sources VRX and VRY. [10 marks] VRX R2

D1

R2

R4

R1 R

+5V

R

R3 VS

X

R3

D2 -VRY Figure 3(a)

VO VS1

VO1 Figure 3(b)

(c) If the output of this functional generator (VO) now is used to provide an input (VS1) to the circuit shown in Fig. 3b, which contains a four-quadrant analogue multiplier (X) with a scaling factor of 0.1, sketch to scale the voltage transfer characteristic (VO1 vs VS) of the overall system over the input range 0 V ≤ VS ≤ +3 V. [8 marks] 4.(a) Describe two main approaches for analogue multipliers. State their advantages/limitations and applications. [7 marks] (b) A four-quadrant multiplier (Gilbert) cell is shown in Fig. 4. (i) Assuming that all transistors are matched and have negligible base currents, show that: I 4 × I6 = I3 × I5 [5 marks] (ii) Find the expressions for the current through the transistors Q1 - Q6 (I1 - I6) as function of VA and VB. [6 marks] (iii) Given that the differential output current I0 = (I35 - I46) =(I3 + I5) - (I4 + I6) = (I3-I6) - (I4-I5) show that I O = − I EE × tanh(VA / 2VT ) × tanh(VB / 2VT ) Note: (ex – e-x) = (ex/2 + e-x/2) (ex/2 - e-x/2) and tanh(y) = (ey - e-y) / (ey + e-y) [7 marks]

IO =I35 - I46

I35 I3

I46

I4 I5 Q3

VA

Q4

I6 Q5

I1

Q6 I2

Q1

Q2

VB IEE Figure 4 5. The 2nd-order phase-locked loop (PLL) system illustrated in Fig. 5 contains sub-elements with corresponding gain values as shown in Table 1. The amplifier gain may be assumed to be constant. Table 1 Gain Component Symbol Value Units Phase Detector KD 100 volts/radian VCO KO 106 Radians/sec/v Amplifier A 20 dB Given loop-filter component values R1 = 1 kΩ, R2 = 100 Ω and C = 1 nF, sketch (a) the asymptotic closed-loop (VO/ωi) PLL frequency response and estimate the bandwidth and [10 marks] (b) the asymptotic loop-gain response and, graphically or otherwise, determine the 0 dB intercept frequency. [9 marks] (c) Explain the advantages of using second–order low-pass filter in PLL system with a help of loop response. [6 marks]

ωi

1/s

ϕi

PD KD

R1 A R2 C

1/s

VCO KO Figure 5