Question

2. In the circuit shown below, the operating frequency for the transmit antenna is 300 MHz. At this frequency, we can represent the transmission line and antenna with a resistive load RL. This resistance accounts for radiated electromagnetic wave. The variable capacitor and inductor shown were tuned to achieve an impedance matching condition, i.e. where ZL is the impedance of the transmission line-antenna assembly and Zr is the Thévenin equivalent impedance of the driver circuit, including R., C and L. For this measurement, assume R, = 300 and the transmission line-antenna assembly can be represented by a resistor and a capacitor as shown. R. V ( L 13.262 pF R. ww 40 (a) Find the values of C and L that achieve the impedance matching condition. 35 points (b) (Bonus 5 points) Calculate the maximum power delivered to the load.

Answer 1

Firstly, the question is purely based on circuit theory. Here the key concept is to know the thevenin theorem.

To find the thevenin circuit - remove the load ie R = 40 ohm and C = 13.262 pF. Next short the input voltage source.

Then find the equivalent impedance across the load terminals, which will give $Z_{t}$

Then for impedance matching - $Z_{l} = Z_{t}^{^{*}}$

Refer below image for solution -

Trinest, let's find the thevenin equivalent empeds Theremin circuit - (for calculating impedance) on Assuming - Fc Xe 21 XL = Lue. CU L Rellc - z = Rut-jxc _ aRgj xe (Rs tj x) " Rejte (@j + c) (R s tj x2) u - As 2 series with XL 7 R2 + x² Rst+x2 8 + x Calculate - z = R series with Xce. Rp = 405, C = 13.262 pF, fgiven 300M Xe = 1 = 1 cw 13.262pF x 211 x 300MHz 4 ZL= 40 -j 40 to get impedance matching condition- 40-40j / R₂ Xc²

40- 40j = R12 quating read & imaginary terms 40 = Rzxc 2 Griver, R3=3002 40=300x2 - 300² + x ² 7. 3600 000 + 40Xc? = 300Xc? 260 4c = 3600000 X = 117.672 = 1 cu e 4.5PF 117.67X27X300 MHZ TER . C= 4 5PF maginary 40 = X-Rexe Subsituling values of 40 = X - = - 300 x 45 117.67 = x - 101.98. 300 + 117.672. X = 101.98+40= 141.982. - 141.98- LX20X300MHZ h = 75.36H in C and L values are - ca 4.50F = 75.3nH.

2. To calculate maximum power transferred

Formula -

$P_{max} = \frac{V_{th}^{2}}{4R_{th}}$

But in this question, Vs ie input source voltage value is not given.

I will explain how to solve if provided.

While finding thevenin equivalent circuit, Vth should also be calculated. It is Voltage across the load terminals. Find Vth.

Use the above formula to calculate maximum power transferred