Question

14F+C RS 10 10022 T-circuit

Assume the load resistor R_L= 100 Ohms. Assume v_S(t) = 1cos(wt). Rs=3ohms, L1=7H, L2=9H, and C=8uF

First, convert the circuit to an impedance equivalent circuit in the phasor domain finding impedances in terms of w. Draw the circuit and mark the impedances.

Then analyze the circuit (you will need to find equivalent impedances and apply voltage division rule) to find the phasor V_L in terms of V_S, and find an expression for g = |V_L|/|V_S|, the gain ratio of the output voltage amplitude to input voltage amplitude. Show your work. If you solve by hand, take a legible photo, paste here as jpg and crop and unnecessary parts.

Then write a MATLAB code which takes in v_S(t) with various frequencies for the range of frequencies from 0Hz to 20kHz, and finds v_L(t) for each of those frequencies, and the computes the gain ratio of the amplitudes |v_L(t)|/|v_S(t)| which is also equal to g = |V_L |/|V_S|.   Use at least 1000 data points for w, within the frequency range.

Plot g versus w: a) using normal scale and also b) in the log g vs log w scale, using the logspace command or loglog command. Type “help logspace” or “help loglog” in MATLAB. Provide the codes and the plots here.

Which plot do you like better, why? Adjust the horizontal and vertical axis limits if necessary, for better viewing.

Inspect the curves, at what frequency does the non-zero frequency “peak” occur?

Why at this particular frequency? Can you find a relationship of this frequency to the circuit variables?

Answer 1

. In jw domain 32 ;7W Vs ♡ p + de sloo Vu j8w 2. C 100 +j)w) x C 100 + j9w) T C100+jgw) 106 706-72w+ j 800w Zin = 34376. 14 100+Jows] = 3+;70 t (100 tj gw) 10€ 106-7262 +j 800w Ve = 2050; TU, RAVE gw)ior Vs Vi = 400 V - 100 Z No. 100+ jgw 100+igw. Zy+3+j gw - ioo (100+; 9W ) x100 - 100 tggu (3+)70)(10%-72w²+;800w) +(180 + jgw)ia6 toke Vs = coswi as ref. then. Vs F1L0. Velw) = 10 13+j7w) (106-7262 +1 80030) +(100+; gw ) X 106 Gain Ration Ni(w) 166 (W) (3+376) (106-7264+j800w) + (100 +jgw)X106

AMATLAB R2015 a G a s E 5 CE Search Documentation 3 fx Eb - D Run Section 8 HOME PLOTS + G A La Find Files Compare New Open Save Print FILE a C: Users Current Folder Name MATLAB Electrical_circuit.m APPS EDITOR PUBLISH VIEW Insert & > Go To - Comment % % % Breakpoints Run Run and ET, Advance Run and Find Indent Advance Time NAVIGATE EDIT BREAKPOINTS RUN Admin Desktop HomeworkLib Editor - C:\Users\Admin\Desktop\HomeworkLib\Electrical_circuit.m Electrical_circuit. m x + - f = 1:20:20000; w = 2*pi*f; den = (3+7*w.*li).* ((10^6) - 72.* (w.^2) + li*800.*w); V = (10^6)./ (den + (100+li*9.*w* (10^6)); plot (V,w) x Workspace Name I den III Value 1x1000 complex double 1x1000 double 1x1000 complex double 1x1000 double Figure 1 File Edit View Insert Tools Desktop Window Help Oddah @ @moda O E-O 104 14 Command Window >> Electrical_circuit Warning: Imaginary parts of complex X and/or Y arguments ignore > In Electrical circuit (line 5) >> fx -1 0 1 2 3 4 5 Details * 10-3 script Ln 3 Col 50
Since the question contains multiple subparts we are asked to do first four of them and hence I am uploading the same.. Thank you