ELEC 240 Lab

Experiment 3.2

Filters and Transfer Function

Equipment

  • Test board
  • \(2.2 k\Omega\) Resistor
  • \(0.33 \mu F\) Capacitor

Part A: Measuring the Transfer Function

Measuring the transfer function of an RC circuit is considerably more involved than measuring the attenuation of a resistive voltage divider. We have to make the measurement at a number of frequencies, and we must measure phase as well as amplitude.

  1. Select a 2.2 \(k\Omega\) Resistor and a 0.33 \(\mu F\) Capacitor.

    Note

    Ceramic capacitors use the same labeling codes as the potentiometers except that the units are picofarads (\(pF\)) instead of ohms. So a 0.33 \(\mu F\) capacitor would be a 330,000 \(pF\) capacitor which would have the code 334 = \(33*10^4\).

  2. Wire the following circuit:

  3. Connect the FGEN to supply \(v_{in}\) and the oscilloscope to measure \(v_{out}\).

  4. Using the technique described in the previous section, measure the frequency response of the circuit at the following frequencies: 20 Hz, 50 Hz, 100 Hz, 200 Hz, 500 Hz, 1 kHz, 2 kHz, 5 kHz, 10 kHz, and 20 kHz.

  5. Plot the magnitude of the transfer function vs. frequency on loglog axes and the phase on semilog axes. This can be done by hand or in Matlab.

  6. Using Matlab, compute and plot the expected transfer function for the circuit you built. How well does this compare with what you measured?

    Caution

    Leave this circuit assembled. We will use it in the next experiment.

Part B: Circuit Simulation

The remainder of the lab can be done from a computer (lab computer or personal laptop). We will be using circuit simulation software called LTSpice. Spice stands for (Simulation Program with Integrated Circuit Emphasis).

  1. Open LTSpice which is installed on the lab computers. If you are using a personal laptop, you can download LTspice here. There are Windows and Mac versions available. Please note that the instructions below are specifically for Windows.

  2. Click on New Schematic and create the same circuit you built on your breadboard by following the instructions on spice provided in the references section.

  3. Perform an AC analysis using the instructions provided in the references section.

  4. Take a screenshot of your plots.

  5. What is the gain at low frequencies (1Hz)? Indicate the gain in dB as well as in V/V. This is called the DC gain.

  6. At what frequency does the gain fall 3dB below DC gain? Thare are many names for this frequency including 3dB, cutoff, or corner frequency. It is also called the half-power frequency, because at this frequency, the output power has dropped to half of its peak value. This half-power frequency defines the bandwidth of the filter.

  7. Notice how the gain plot is linear with a negative slope beyond the cutoff frequency. What is the slope of the gain plot at high frequencies (\(>1kHz\))? Express in terms of \(dB/dec\). This is called the gain rolloff.

  8. What is the phase for very low frequencies? And for very high frequencies? Can you explain why?

  9. Now cascade another lowpass filter to your circuit:

  10. Run an AC Analysis of this new circuit, and click on its output node to display gain and phase plots (the output will be at the node between R2 and C2). Take a screenshot of your plot. What is the new gain rolloff (\(dB/dec\))? The phase at low and high frequencies?

  11. Did the cutoff frequency change?

  12. What are the pros and cons of cascading two identical filters?