# Transfer Functions

1. May 9, 2010

### Fronzbot

1. The problem statement, all variables and given/known data
Determine the transfer function for the circuit shown in figure 5 if the output voltage is defined as the voltage drop across the 20$$\Omega$$ resistor. Note there are two sources in this circuit.

2. Relevant equations
H(s) = $$\frac{Vo}{Vi}$$

3. The attempt at a solution
From the previous question (I needed to find the Voltage and Current across the Inductor and the voltage across the Capacitor all in the 'S' domain) I know that, assuming Vbis the node voltage where the cap, inductor and resistor meet, Vb=$$\frac{120(5s^2+20s+11)}{s(s^2+5s+6)}$$ and, assuming Va is the node voltage at the current source, Va=$$\frac{60(11s^2+51s+22)}{s(s^2+5s+6)}$$.

Now what I'm having trouble with is determining what I should use for Vi. Every problem in my book or in class has defined an input voltage somewhere and all of them have only ever had one source. My idea is that I could use superposition to find the transfer function so I determine Vo when the current source is opened and Vi=$$\frac{60}{s}$$V and then add that to the transfer function when the voltage source is shorted and Vi= Va. Is this a valid approach?

Last edited: May 9, 2010