What is the maximum unilateral transducer gain in db -

Question

Question 1:

Consider the following wireless receiver chain consisting of a low noise amplifier (LNA), bandpass filter and mixer, as depicted below. The LNA receives its input signal from an antenna.

a) If the input noise power P_nin from the feeding antenna is kT_AB, with T_A=150 K, find the output noise power in dBm.

b) If a signal-to-noise ratio of 20dB is required at the output of the chain, what is the minimum root-mean-square (rms) signal voltage that can be applied at the receiver input? Note: Assume the entire system to be at a temperature of T₀ = 290K, with a characteristic impedance of 50Ω, and an IF bandwidth of 10 MHz.

Question 2:

An amplifier uses a transistor that has the following S-parameters at an operational frequency of 5.4 GHz (Z₀ = 50Ω): S11 = 0.61exp(-j170°), S₁₂ = 0.06exp(j70⁰), S₂₁ = 2.3exp(j80°), and S₂₂ = 0.72exp(-j25⁰).

The input of the amplifier is connected to a source with VS 2V (peak) and Zs=250; the output is connected to a load of Z_L = 100L).

a) What are the input and output impedances of the transistor? Please report your answer in real and imaginary parts.

b) Find the operating power gain, the available gain, the transducer gain, and the unilateral transducer gain, all in dB.

c) Compute the available power from the source and the power delivered to the load in dBm.

Question 3:

Design an amplifier with maximum unilateral gain using a BJT with the following S-parameters at 6 GHz (4=500):

S₁₁ = 0.61exp(-j170°), S₁₂= 0, S₂₁ = 2.24exp(j32°), and S₂₂ = 0.72exp(-j83°).

a) What is the maximum unilateral transducer gain in dB?

b) Design two-element matching networks with lumped components. Sketch all choices for the input and output sides.

c) You are now asked to dimension i) an input matching network (IMN) that, starting from the source, involves a shunt L and a series C configuration and ii) an output matching network (OMN) which, starting from the load, involves a shunt L and series L configuration. What are the component values? Sketch both matching circuits and label all components with values in nH and pF.