Complex Circuits II

1. Build a voltage divider:

a. Suppose you have a fixed voltage supply that puts out only 9V, yet you need a 3V source: how can you reduce 9V to 3V? Choose any two resistors that will allow you to build a voltage divider which will supply you with 3V (across one resistor) if the power supply is 9V. Build this circuit in Multisim. Notes:

1. We are pretending that our normally variable power supply is fixed at 9V - be sure to adjust your power supply to be 9V.

2. Let's assume that that these are 1/4 Watt resistors - that is the maximum power that they can use/produce before they get damaged - which means if any one resistor is subjected to 9V, the smallest resistance you should use is 364 Ohms.)

3. Your goal is to have a potential difference across the resistor attached to the "ground" side of the power supply be 3V (which we generally choose to be the negative side of the power supply). The reason we choose this resistor rather than the other one is that while electric potential difference (voltage) is not dependent on where the "ground" is, the electric potential anywhere in the circuit does depend on where the "ground" is. Remember that when we are discussing potential energies and related quantities, we always measure relative to zero, and we can define where we want that zero to be. "Ground" is where the electric potential is equal to zero. So if the right side of the battery in the image below is at a potential of 0, then the spot in between the two resistors is at a potential of 3V, and the far left of the circuit is at 9V. Note that while the potential difference across the resistor on the left is 6V, the potential is not 6V anywhere in the circuit.

b. You have now reduced your voltage to a useable level by using the voltage across your smaller resistor as your power supply. Make sure to measure the voltages everywhere to be sure it is working as expected.

c. The power used by a resistor is P = IV, where I and V are the current through the resistor, and V is the potential difference across the resistor. Determine the power used by each of your resistors in your voltage divider.

d. Lets use your voltage divider as our new power supply. Choose a resistor that is a lot larger than the smallest resistance in your circuit, and pretend this is the "device" we need to power. Hook up your chosen device to the 3V power supply you have created, and measure the voltage across your device. Hopefully, it is near 3V as expected. Determine the power used by your device.

e. Repeat the last step (d.) with a resistor ("device") about equal to the smallest resistor in your voltage divider, and note what about it indicates that your voltage divider is not working as desired.

f. A voltage divider is a quick and easy way to reduce a fixed voltage, but what are the drawbacks? (You may learn later that with AC power, you can use a "lossless" transformer to reduce the voltage instead of a voltage divider.)

2. Build a low-pass filter and determine the cutoff frequency:

A low pass filter takes an AC signal as an input (which has an amplitude and a frequency, such as a sine wave) and outputs an AC signal that is similar to the input only if the frequency is low enough. If the frequency is too high, the signal amplitude will be attenuated (will be made smaller). Hence it lets low frequency signals pass through the circuit, but filters out high frequency signals.

A radio is an example of a device that filters out signals with frequencies higher than a certain number (low-pass filter), but also filters out signals with frequencies lower than a certain number (high-pass filter), in order to pass through signals of only a short range of frequencies. That is, if you want to listen to a radio station at freuency 91.5 MHz, you want to filter out the station at 95 MHz, and filter out the station at 89 MHz. When you have both a low-pass and a high-pass filter together, it is called a notch filter.  

1. Build the same RC circuit as last lab. Notice that the RC circuit is actually a lot like a voltage divider, and we are essentially going to use it like that. In a low-pass filter, we are using the capacitor as the part of the divider that we are taking the signal from, so the capacitor has to be on the ground side of the power supply (that is something we stressed a lot in the original RC circuit lab). Using a sine wave (instead of square wave or DC voltage) from the power supply, measure the voltage output across the capacitor, as we did last week and compare it to the output of your power supply as follows:

   1. We are using an AC power supply with an R and a C in series like in the last lab, being careful to define where ground is.

   2. You can use whatever R and C you want, but perhaps choose a combination such that the time constant RC = 1 ms or lower. Whatever R and C you use, be sure to note what the values are.

   3. Set voltage of your power supply to be non-zero, as long as it is big enough to be a readable signal it does not really matter what it is, and be sure to measure the output of your power supply directly with the oscilloscope - make sure you can read the amplitude of the potential difference (voltage) from the graph.

   4. In order to use the filter, you are then going to measure the amplitude of the potential difference across the capacitor. Use the other channel (presumably channel 2) on the oscilloscope to measure this. Remember, the channels are simply separate voltmeters, these oscilloscopes just have two channels that allow you to measure two voltages at once. 

   5. Compare the amplitude of potential difference across the capacitor with the potential difference supplied by the power supply. If the amplitudes are the same, then you are at a frequency that is low enough that the signal is allowed to pass. If the amplitude is smaller for the potential difference across the capacitor, then that particular frequency is being filtered - we are flitering out some of the signal. Vary the frequency of your power supply and do this comparison for a range of frequencies, being sure to find a frequency for which the potential difference is not attenuated, and another frequency for which it is, and keep track of the frequencies and corresponding amplitudes of the potential differences.  

2. The "cutoff" frequency is defined as when the output is 70% of the input. Determine the cutoff frequency of your circuit.

For your lab notebook or writeup, be sure to record all values of measurements (R, C, V, f), make diagramsof any/all your circuits, and keep pictures of the oscilloscope output.