5/26/16 - Transfer Functions

Today we learn about transfer functions, which are functions dependent on frequency.

It can be expressed as gain, impedance, or admittance. With the units of potential over potential or current or current magnitude for gain, or potential over current or visa versa for impedance or admittance.

We do a simple current divider equation to find the ratio of the current input versus output.

Replacing the jomgas (j * omega) with s, we can find the transfer function and then solve for poles and zeros.

Another problem were we use nodal analysis to solve for the gain as a transfer function. We find there is a zero at 0 and a pole at -1000.

Plugging this into a log plot, we can see clearly see where the pole is, as well as the zero at 0.

Another circuit, this time the components are in series, we use a voltage divider to find the transfer function and solve for zeros and poles.

Since the poles are at -100 and -10^6, two separate log plots were used to see the poles and zeros.

For our lab exercise, we hook up a resistor in series with a capacitor and resistor in parallel and are going to measure the voltage across the the resistor in parallel.

Here the circuit set up.

First we fed it the sum of two different sinusoidal signals and observe its output. The blue is the input signal and the yellow is the measured signal. We can see that the yellow is slightly out of phase due the jimaginary component of the capacitor and the gain is roughly 1/4.

The scale of the graphs to show the gain of 1/4.

Our calculations for the output.

Next we feed different frequencies to the circuit.

V = 20[sin(1000πt) + sin(2000πt) + sin(20,000πt)]

Here we calculate our expected voltage from the output.

For 1000Hz.

For 10000Hz.

Lastly, we feed a sweep function into the circuit. A sweep function is simply a sinusoidal signal that increases in frequency over time and repeats itself.

We can see the input signal versus the output signal and we see that as the frequency increases, the less impedance the capacitor has and more potential is across the capacitor than the the resistor,

Our scales for the above graph.