Question

Using the indicated parameters for each system element (P in, G1, L & G2) and with impedances matched for each junction (node, Ni ) of this end-to-end system, compute a) the net linear system gain, b) the net system gain in dB, and c )the power levels (in dB) at each stage of this cascaded system (i.e. Pin, N1, N2, and P out). Pin=0.1 W, G1=400, L=2,000, G2=500

Answer 1

Given P_in=0.1W G1=400 L=2000 G2=500

Since the values don't indicate the Shunt admittance and Inductor and also since the fig: is not given I am not assuming this as a pi network (transmission line model), rather a linear system as shown below

Assume the gains given are power gains.

Pin ----[G1]------(N1)------[L]-----(N2)---------[G2]------Pout

Since impedances are matched for each junction/node the gains can be multiplied and the power gets halved at the junction.

(For more detail scroll further down).

(a) The net linear system gain = G1x(L/2)X(G2/2) = 1 x 10⁸

(b) For power amp Gain(dB) = 10 log(Gain). Here our answer will be 80dB

(c) The power level in each stage is the power at the preceding stage times the gain at the present stage. At N1 it's 0.1x G1(dB) = 2.602. At N2 it's 0.1*(G1*L/2)(dB) = 5.602. At Pout it's 0.1*80 = 8

As per the power transfer theorem, maximum power is transferred occurs/ minimum signal reflection from the load occurs when the input impedance and load impedance are complex conjugates of each.

Don't get confused with max power transfer theorem and maximum efficiency. They are different.

For maximum efficiency output impedance must be infinity or input impedance can be zero. In that case, we could have just multiplied the gains.

For maximum power transfer, we need the impedances to be complex conjugate and hence the power transferred will be half the input power.