How to calculate transistor gain for pnp

[Jerry James]

hi

how to calculate the gain of collector to base bias circuit using a pnp transistor? I am using BC 558, Rb= 1M, Rc= 4.7k , Vcc= 9V.

[Jerry]

BC 558 PNP base biased

Rb = 1 Meg

Rc = 4.7K

Vcc = -9v  Notice that Vcc for this circuit needs to be negative.

The question is how do we determine the DC gain or Beta of this circuit.  The short answer is we look in the datasheet but the datasheet shows the typical gain as 120 to 400.  This is a pretty big range.  Let’s see what we can calculate.  We can find Vb (base voltage) because it is one diode drop from ground.  So Vb is -8.3 volts.  Now that we know Vb we can find Ib (base current).  Ib = Vb / Rb = -8.3v / 1M = -8.3uA.

Now the only way to determine our Beta (DC Gain) is to measure the voltage at the collector.  So let’s say our collector voltage is -1.2 volts.  Now we can calculate the collector current by Ic = (Vcc – Vc) / Rc = (-9 – (-1.2)) / 4.7K = 1.66mA.  Now that we know the collector current we can calculate the Beta (DC Gain).  Beta is equal to the collector current divided by the base current.  Beta = Ic / Ib = 1.66mA / 8.3uA = 200  So we have a Beta of 200