Day Twenty-Four - Signals with Multiple Frequency Components

Hello guys, today we talked about transfer function.
The transfer function is simply the ratio of some output to some input in a given frequency.
From the transfer function, we can know more about the ratio of something over something with different frequency.

Since the range of frequency is wide, a Bode plot is used instead to simplify the range of the frequency.
One important point to note is that 10log is used for power while 20log is used for current and voltage.

Here is an example of how we calculate the transfer function of the circuit above.

Pre-Lab:
The response of the circuit with 2 680 ohms resistors and 0.1microFarat capacitor has the following result:

From the data above, we can conclude that as the frequency increases, the voltage gain decreases.

Result:
The voltage output and input have the following signals.

The yellow indicates the output voltage across the resistor, and the blue indicates the input voltage of the circuit.
As we can observe, the waveform has a shape of multiple waveforms into one waveform, and the voltage input and output have the similar pattern. We can also observe that low frequency signal has a bigger magnitude of gain while a high frequency signal has a smaller magnitude of gain.

Using the sweep function of the waveform, we get:

 This graph shows the gain of different frequencies signal, from 100Hz to 10kHz.
We can also tell from the graph that when the frequency is low, the gain is relatively small, and when the frequency is high, the gain is relatively big.

Summary:
The transfer function can give us a very intuitive meaning of how the circuit will respond when the frequency increases or decreases. Another important point to note is that in Part a, the three waveforms are combined together to generate one waveform, and the shape of the three waveforms are still observable. For the circuit we used in our lab, we can conclude that the circuit is a low pass filter because it has a high gain in low frequency but low gain in high frequency.