To EE222 Class and Whoever is Interested

From Doug Hoffman

Lab partners Steve Pietrucha and David Strickland

Lab 9

### Introduction to Amplifiers Input Resistance, Output Resistance: What They are and Who Really Cares

In this lab we are introduced to the amplifier. All of us have heard of amplifiers and many of us have seen or used them. However, not many of us really know how or why they work. In this lab we will investigate the ideas of input and output resistances for the amplifier, as well as sources and loads. We will see how they affect the circuits we use.

The first step of the lab was to measure the output resistance from the HP function generator. With the function generator "on" we measured the resistance using the Fluke as an ohmmeter. We took this measurement with the function generator "on" because this is the only time we really care about the output resistance. We found the resistance to be 50 ohms, the value at which the function generator is rated. To check this value we measured the open circuit voltage (Voc) as well as the output voltage (Vo) when a 20 kohm resistor was attached to the output. Modeling this as a Thevenin equivalent circuit, we found the output resistance of the function generator to be 56 ohms. See calculations. The Thevenin model is probably a better method to find the output resistance. This is because we usually only worry about what the output resistance of the function generator is when we have a load attached to it.

The next step in our lab was to connect the earphone-jack of our portable stereo "Walkman" to a speaker. Listening to the music from the speaker we found that it sounded very bad (not just because it was Frank Sinatra singing) and was not very loud even though it was at maximum volume. We then measured the resistance of the speaker (Rload) using the Fluke and found it to be 7.6 ohms. To find the output value of the "Walkman" we again wanted to use a Thevenin equivalent model. However finding the open circuit voltage (Voc) and output voltage (Vo) were much more difficult this time. This was caused because, unlike the function generator which outputted a simple sine wave, the stereo outputs a signal which has many amplitudes and frequencies. To find Voc and Vo we used the oscilloscope and sampled a small portion of music, without and with the speaker attached respectively, and took the average voltage over the time. To insure that our Voc and Vo corresponded to each other we sampled the same bit of music. This bit was when Old Blue Eyes himself sang the "Oh come" part of the song "Come All Ye Faithful" (sorry we didn't have much to choose from). Anyway, using our Thevenin model we found the output resistance of the stereo to be 8.32 ohms. See calculations.

The last step in our lab was to measure the input and output resistances of the HP 6825A amplifier. We found the input resistance to be 7.6 kohms while the output was only 2 ohms. When we hooked our stereo to the input of the amplifier and the speaker to the output we found that the music sounded pretty good, even for Frank Sinatra. We found that we could also vary the gain just by changing the degree of amplification. This phenomenon can be explained by simply thinking of our stereo and speaker as two resistances in series and using a voltage divider equation. Before we calculated the output resistance of the stereo to be 8.32 ohms while the resistance of the speaker was only 7.6 ohms. Putting these two resistors in series we can see that over half the applied voltage will be dropped in the stereo before it even reaches the speaker. When the amplifier is used we now have a 2 ohm resistor in series with our 7.6 ohm speaker. Now almost 80% of the voltage is dropped across the speaker, which causes the music to sound much better.

These results make you wonder why our earphones for our "Walkmans" do not come with amplifiers. This is because earphones usually have resistances several times higher than the speaker we used. In fact, one good pair of earphones we measured had a resistance of 32 ohms. These connected to the stereo with an output resistance of 8.32 ohms would give the same 80% voltage drop across them as the amplifier did.

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