Transistor Analysis

In this experiment we are asked to determine the gain of an npn transistor of type 2N3904 using the following circuit configuration.

In order to find the gain for this transistor, we need to understand a little more about how a transistor works. For more information on the inner workings of a transistor see this link. Now that we know what a transistor is, we are interested in analyzing it in our circuits. A transistor can be modeled as a current dependent current source, an independent voltage source, and a dependent voltage source.

Here is a picture of the equivalent circuit.:

Important to note about this image, the voltage across V5 is usually .7V while the transistor is in its active mode. The dependent current source I1, and the dependent voltage source V6 are undetermined until the current through R6 is determined. At that point the current through R6 can be multiplied by the gain, and the current through I1 is the result. Both currents sum together and travel through V6 to ground. The hard cap on the current through I1 is partially determined by the transistor, and also by V3 and R7. By inspection, it is easy to note that the current through R7 can never exceed 60 mA, because in order to do so each element after it would have to have negative resistance. (the maximum voltage is 6V, divide by 100 to get 60 mA)

In order to determine the gain of the transistor in question, we will want to test currents well below 60mA in order to preserve the linear relationship between input current and output current. In the original configuration, the simulation predicts a base current of 162.11 uA and a collector current of 25.37 mA. This corresponds to a gain of approximately 150, and the current through our limiting resistor is not nearly reaching the theoretical maximum. The next step is to take some data to verify if this circuit element has similar properties to the element we have in the lab.

Using a variable resistor box, 2 Digital Multi-Meters and a 2n3904 transistor we took several data points for base current and collector current, the results can be found in the table which follows, and pictures of the setup are shown below.

 Pictured above: the experimental setup, including the all important coffee cup.

 The above tangle of wires sends current to the transistor, away to the meters, and does not look anything like the nice schematic from earlier.

It is evident from the data collected that the gain is converging to some real number, and this is more evident from a plot of the collector current versus base current.

The graph has a decidedly linear appearance, and a non zero intercept.

Due to the limitations of the input resistor, the circuit configuration will saturate at about 247uA or nearly 2.5 times the maximum input current in our data. Although the transistor may exhibit highly non-linear behavior as the base current approaches this value.

According to the graph, the transistor we used had a gain of approximately 250, meaning that the spice model from earlier used a transistor with a different gain. If we are going to simulate any circuits using this transistor, we will either need to find the appropriate model in the libraries, or make a new model based on the existing part but with a higher gain.