Electronics: A Guide for Physicists (DRAFT -- in development)

Introduction.

The operation of many electronic devices depend on a DC voltage source, but the electricity delivered to households in the United States is 60-Hz AC voltage. Today, we’ll explore one method of converting AC voltage to DC voltage using the bridge full-wave rectifier with a smoothing capacitor as pictured in Figure 14.6.1.

This circuit converts an AC input voltage to a nearly-constant output voltage, though a small ‘ripple’ will remain. Larger values of smoothing capacitance will reduce the size of this ripple and thus will improve the quality of the DC voltage output. High-capacitance capacitors are typically more expensive and physically larger than small capacitors, so there is incentive to keep the capacitance as small as possible. Thus, devices that require DC voltages often specify a maximum ripple size that they can tolerate.

EXPERIMENT.

1. Use your DMM to determine exact values for your resistor and your capacitors.
   Warning: The capacitors that you are using are called ‘electrolytic capacitors’ and are polarized, meaning that they only work when the negative lead (often marked with a negative sign) is at a lower voltage than the positive lead. When measuring the capacitance with the DMM, connect the COM to the negative capacitor lead.
2. Unplug your prototyping board. You will not need to plug it in for this experiment.
3. Construct the circuit shown in Figure 14.6.1 on your prototyping board. Use the smallest capacitor value that you’ve been given as your smoothing capacitor. The input voltage \(V_\text{in}\) will be provided by your function generator.
   Warning: Pay attention to the capacitor polarity in the circuit schematic. If you wire the capacitor in backward, you can destroy the capacitor (sometimes resulting in a puff of smoke or small flame). Remember that in this circuit, \(V_2 \gt V_1\) always.
4. Set up the oscilloscope to measure \(V_\text{in}\) on CH1 by connecting the oscilloscope probe to the proper location in the circuit that you constructed. Turn your oscilloscope on.
5. Turn on the function generator (but leave the OUTPUT off). Set the generator to produce a 120-Hz sinusoidal voltage with a peak amplitude of 5-V. Then, enable the OUTPUT.
6. Use the CURSOR functionality to measure the amplitude of \(V_\text{in}\text{.}\)
   Q: Record your \(V_\text{in}\) amplitude in your lab notebook.
   P: Insert a photograph of \(V_\text{in}\) into your lab notebook.
7. Disable the function generator OUTPUT.
8. Set up the oscilloscope and probes in the following way.
   Warning: Failure to follow these instructions may result in equipment damage and/or electric shock.
   • Use an oscilloscope probe (x1) to connect CH1 across \(V_2\) and ground.
   • Use an oscilloscope probe (x1) to connect CH2 across \(V_1\) and ground.
9. Enable the function generator OUTPUT.
10. Use the oscilloscope’s MATH functionality to display \(V_\text{out}=V_2-V_1=\text{CH1}-\text{CH2}\) on the oscilloscope screen. Under the MATH menu, do the following:

    • Set ‘Operation’ to ‘\(-\)’.
    • Set ‘Source A’ to CH1.
    • Set ‘Source B’ to CH2.
    • Ensure that ‘Invert’ is set to Off.
    • Explore ‘Page 2/2’ of the MATH menu. Determine how to shift the displayed MATH signal up and down on the oscilloscope screen and how to adjust the vertical scale for the MATH signal.
11. Use the oscilloscope cursors to measure the size of the ripple on \(V_\text{out}\text{.}\)
    Q: Record the ripple size and smoothing capacitance in your lab notebook.
12. Disable the function generator OUTPUT.
13. Swap out the smoothing capacitor for the next largest capacitance that you’ve been given.
14. Enable the function generator OUTPUT and measure the size of the \(V_\text{out}\) ripple and record this value in your lab notebook.
15. Follow the procedure to measure the size of the \(V_\text{out}\) ripple for all capacitor values you’ve been given, recording the values in your notebook. WARNING: You must disable the output of the function generator before making any changes to the circuit in order to avoid shocks.
16. Use Python to do the following:

    1. Perform a curve fit to your data. Assume a function of the form \(\left(\Delta V\right)_\text{ripple}=AC^B\) where \(A\) and \(B\) are fitting parameters and \(C\) is your capacitance variable.
    2. Plot ripple voltage size vs smoothing capacitance and use symbols to display your data points. Overplot a line representing your curve fit.
    P: Include your plot in your lab notebook.
    Q: Provide your fit parameters in your lab notebook.
17. Predict the minimum smoothing capacitance one would require to ensure a 5% ripple on \(V_\text{out}\text{.}\)
    Q: Include this result in your lab notebook.