EA3_rlc - EA3: Systems Dynamics RLC-CIRCUIT: TONE CONTROL...

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EA3: Systems Dynamics Electrical Systems Sridhar Krishnaswamy 21 RLC-CIRCUIT: TONE CONTROL Figure : A graphics equalizer (courtesy EA3 hyperbook) Most of you have used a graphics equalizer to alter the bass and treble of music that for some reason you do not like to hear the way the composers mixed them. The heart of this device is a bunch of RLC circuits. Each of these selectively passes certain frequencies of the input signal (the music) to the output for subsequent amplification and output to speakers. Here is one such RLC circuit. Figure : RLC-circuit State Variables: X = V C i L { } T Dynamic Rules: KCL: i L = i C = i R KVL: V L + V C + V R = V in Note also that: V out = V R = Ri R = Ri L We will actually plot Vout since this is what is being output by the graphics equalizer circuit to the amplifier etc. ground i L i C i R
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EA3: Systems Dynamics Electrical Systems Sridhar Krishnaswamy 22 State Equation: The first order state equation for the above tone-control circuit you should be able to show is: dV C dt di L dt = 0 1 C - 1 L - R L V C i L + 0 V in L You can feed the above to a MATLAB code given an input signal and the parameters of the circuit. The following code takes a 2 second clip of Handel’s Messiah as the input V in (t). The music is sampled 8192 times a second, and looks like: . We %EA3 % clear all; close all; global A F; %share these with function frate_fn which computes Xdot=AX+F We feed this to the M-file tone-control.m : %% %%System parameters L = 0.00005; %element 1 - mass C = 0.0001; %element 2 - capacitor R = .1; %element 3 - resistor %L = 0.005; %element 1 - mass %C = 0.0001; %element 2 - capacitor 0 2000 4000 6000 8000 10000 12000 14000 16000 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Time-step; each step = (1/8192)s V in (t)
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EA3: Systems Dynamics Electrical Systems
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This note was uploaded on 04/17/2008 for the course GEN_ENG 203 taught by Professor Krishnaswamy during the Fall '08 term at Northwestern.

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EA3_rlc - EA3: Systems Dynamics RLC-CIRCUIT: TONE CONTROL...

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