How does the Early effect limit the voltage gain?

Question

As far as I understand, the Early effect increases the quiescent \$I_C\$ for a given \$V_{CE}\$.

At the same time texts treat this effect as a limiting factor for the gain.

Here is an excerpt from a text:

There is one additional quantity we will need on occasion, although it is not derivable from the Ebers–Moll equation. It is known as the Early effect, and it sets important limits on current-source and amplifier performance.

Another text says:

Does another mechanism in the circuit, perhaps in the transistor, limit the maximum gain that can be achieved? Indeed, the “Early effect” translates to a nonideality in the device that can limit the gain of amplifiers.

But the Early effect increases \$I_C\$ so it must also increase the transconductance which is $$g_m = \frac{I_C}{V_t}$$

So if I'm not mistaken, the Early effect causes an increase in the transconductance. But why then is it treated as if it limits the voltage gain?

Answer 1

Voltage gain for a common emitter amplifier (for instance) is determined in part by the collector resistor. Put simply, the higher the value of collector resistor the more output voltage signal for a given input signal.

For an ideal BJT with no early effect, once the BJT is operating in its active region, the slope of \$I_C\$ versus \$V_{CE}\$ is zero: -

Image from here.

Now flip this around and ask what the collector output impedance of the ideal BJT is; it is infinite i.e. for any change in \$V_{CE}\$, the change in \$I_C\$ is zero. The non-ideal BJT situation looks more like this: -

Image from here. In other words the collector has a high (ish) output impedance but it's not infinite.

And, the early effect makes the slope more pronounced as the collector current rises: -

Image from here. So, early effect can be said to be a gain-limiting factor because this non-ideal resistance is in parallel with the real collector resistor.

Answer 2

Effectively the rising Ic curve means in AC analysis extra resistor between C and E. In common emitter amplifier application it reduces the AC voltage caused by AC component of Ic. That's because the extra resistor must be considered to be in parallel with the load.