# Confusion in the difference between DC current gain and AC current gain in common emitter amplifier

Here is a definition: It is easy to understand what DC current gain means here. The base current is constant, the collector current is also constant. An their ratio βdc = Ic/Ib. This is the DC current gain.

But I don't get the meaning of the βac AC current gain formula here. Is that the derivative of Ic wrt Ib? I came across the following plot but still didn't get how to calculate this gain. How would one practically calculate this if one knows the input and output currents? Imagine the base current Ib is a sinusoidal current signal with 10uA peak to peak; and Ic is 1mA peak to peak. If it was DC current we would say the beta is 100. But here since we are dealing with AC, we need to find the AC gain by looking at the Ic Vce characteristics. How can we progress and make a logical derivation of AC current gain from this point?

## 1 Answer

There is no difference in your graph

• you are absolutely right. the Ic/Ib slope would be constant and equal to beta_dc considering my plot; however in the real one you provided the Ic/Ib slope varies when the signal varies. so as far as i understand beta_ac is quite close to beta_dc even-though it varies with the signal's variation. but wouldn't it cause distortion? if so do that kind of distortion exists in all ICs? – HelpMee Nov 20 '16 at 3:06
• If d(Ic)/d(Ib) has a near-constant value, there's no distortion, so distortiion is in the second and higher derivatives d^2(Ic)/d(Ib)^2 is the curvature, and it looks rather small over a large collector current range. Temperature dependence of gain is a much greater effect. Consider what effect an emitter resistor will have. – Whit3rd Nov 20 '16 at 5:17
• re:2222 > there is significant hFE distortion all above 10% of the maximum current starting at Ic=10,30mA for Vce=1,10V and changing to a negative slope > 50mA @25'C. This is the chief cause of THD for large current swings in all BJT's. THIS is what makes a General Purpose Transistor, different, from one known for excellent Linearity. This is also the reason why Vce>2 to 2.5V is a design criteria for ultralinear Power Amps to avoid the hFE reduction towards saturation. ( but latter part is shown in datasheet for hFE vs Vce) – Sunnyskyguy EE75 Nov 20 '16 at 6:27