Current, Resistance, Voltage, and Power Gains

Author: Leonard Krugman

In the average point-contact transistor, an increase in emitter current of one milliampere will cause an increase in collector current of 2.5 milliamperes. In physical terms, this indicates that one million holes injected by the emitter causes 2.5 million electrons to be injected by the collector. One million of the collector electrons neutralize the holes. The remaining million and a half electrons flow to the base.

The ratio of change in collector current to change in emitter current is called the current gain α (Alpha). Thus

α = I_c/I_e

where α = current amplification, i_e = change in emitter current, and i_c = resulting change in collector current.

In the typical case described above,

α = 2.5 mA/1.0 mA = 2.5

At first glance, the current gain factor of a transistor is disappointingly low when compared with the amplification factor of a vacuum tube. However, another consideration enters the picture: The input resistance between the emitter and base is relatively low (300 ohms is a typical value), while the output resistance between collector and base is relatively high (20000 ohms is typical). Thus, in addition to the current gain, the transistor has another gain characteristic, namely the ratio of output resistance to input resistance. For the typical point-contact transistor, the resistance gain is 20000/300 = 67.

Since the input voltage is the product of the emitter current and the input resistance, and the output voltage is the product of the collector current and the output resistance, the transistor voltage gain equals the current gain times the resistance gain.

where:

e_i = input voltage, e_o = output voltage,
i_e = emitter current, i_c = collector current,
α = current gain, r_o = output resistance, and
r_i = input resistance.

For the typical case under consideration, the voltage gain equals 2.5 × 67 = 167.5. Furthermore, since the input power is the product of the input voltage and the emitter current, and the output power is the product of the output voltage and collector current, the transistor power gain equals the current gain squared times the resistance gain.

For the typical transistor, the power gain equals (2.5)² (67) = 419.