Calculating the frequency response of filter with a matrix

Dethoven · Apr 22, 2016

Homework Statement

This is actually part 3 of the question. Part one was to form 7 equations to form a 7x7 matrix, part 2 was to solve it, which I've done. This question is to be done with Matlab, by the way.

Circuit schematic of a resistive ladder network with voltage source v0, nodes v1, v2, v3, resistors R1, R2, R3 in series and R4, R5, R6 to ground, branch currents i1 to i4, and the caption asking for values of v1, v2, v3, i1, i2, i3, i4 when v0 = 10 V.

Part 3:

Circuit schematic of a multi-stage LC ladder filter with input source v0(t) = v00 cos(2πft), series inductors L1, L2, L3, shunt capacitors C1, C2, C3, resistor R2 at the output, and labelled node voltages v1, v2, v3 and currents i1 to i4.

Homework Equations

Frequency response = V_out / V_in.

The Attempt at a Solution

I know the frequency response is the ratio of V_out and V_in, in this case, v₃ and v₀, I'm not sure how to incorporate that with the matrix I have. I could replace the resistor values with the impedance of the corresponding elements, but since the frequency is unknown, that wouldn't work. I've calculated frequency responses before, but that was for simpler circuit in which I could use the potential divider formula.

donpacino · Apr 24, 2016

calculating the frequency response at one frequency would get you one one point of the graph.
What if you compute 10 different frequencies?
What if you compute 100?
or 1000?

you can still use the same equations you used for the previous parts.

By the way you might want to show everyone the equations you got

Calculating the frequency response of filter with a matrix

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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