# BJT Amplifiers

• BJTs make excellent amplifiers when biased in the forward-active region
• Transistors can provide high voltage, current and power gain
• DC biasing stabilises the operating point
• DC Q-point determines
• Small-signal parameters
• Voltage gain
• Input & output impedances
• Power consumption
• DC analysis finds the Q-point
• AC analysis with the small-signal model is used to analyse the amplifier

## Hybrid-Pi Model

The hybrid-pi small signal model is what is used for hand analysis of BJTs: • Intrinsic low-frequency representation of a BJT
• Does not work for RF stuff
• Ignoring output impedance assumes is large
• Parameters are controlled by the Q-point
• Transconductance
• Thermal voltage
• Input resistance

For AC analysis, coupling capacitors are replaced by short circuits, and DC voltages replaced by short circuits to ground. The circuit below shows a 4-resistor bias amplifier replaced by it's small signal model. ## AC Analysis

The impdance at the base input :

The impedance at the emitter is reflected back to the base, multiplied by . This makes the overall input impedance of the amplifier:

The output impedance is easy, as lookong into the collector, we can see in parallel with a current source which has infinite impedance, so:

The voltage accross is the output voltage:

The voltage accross is the input voltage:

The overall voltage gain is therefore:

Note that the gain is negative meaning this is an inverting amplifier. If we make the assumption that , and that is large, then:

## Common Collector Amplifier

The common collector (or emitter-follower) amplifier is another amplifier circuit used with BJTs (as oppose to the common emitter shown above). The hybrid-pi model of this circuit looks like, as without the collector the circuit can be re-arranged to: The output voltage is the voltage accross the emitter resistor, and as :

The input voltage is the voltage accross both the emitter resisitor and :

Therefore the voltage gain for this amplifier is:

As usually, , . This amplifier has very low voltage gain, and instead acts as a current amplifier:

The input impedance is large, as it is the reflected impedance from the emitter resistor again:

The output impedance can be calculate by shorting , and by applying a test current source accross the output terminals. I'm not going to type out all the analysis but:

The emitter follow has high input and low output impedance with a high current gain, so acts as an impedance transformer and a buffer.

## Example

A circuit for a common-emitter amplifier is shown below. Work out the values of the DC biasing components , , and for the following conditions:

• Voltage accross

Assuming and , we have:

Calculating the Thevenin equivalent of the biasing resistors:

Then calculating the bias resistors from the Thevenin values:

To derive an expression for the voltage gain, need to replace the BJT by it's small signal model 