25.2.4. Considering Early Voltage Effect

So far, we are ignoring the early voltage effect namely the dependency of the collector current on the V_ce we are ignoring. But in case if we want to consider whatever the dependency, it is having slight whatever positive slope in the active region and this slope will be represented by finite conductance ∂I_C called g₀ ∂V_ce.

The Early Voltage Effect refers to the phenomenon where the collector current (I_C) varies with changes in the collector-emitter voltage (V_ce). In a typical scenario without considering the Early Voltage, we assume that the output current remains constant regardless of the voltage, leading to a simplified model. However, as we factor in this effect, we notice a slight positive slope in the active region of operation, which suggests a dependency exists. This dependency can be quantified using a parameter called g<sub>0</sub>, which reflects the change in collector current for a small change in V_ce.

Think of the Early Voltage Effect like a car that accelerates faster when it goes downhill (increased V_ce), versus when it's driving on flat land. Just because there's a constant speed (the idea of fixed collector current) doesn't mean it won't speed up with a change in the slope of the road!

And this is called small signal reciprocal of small signal output resistance r_o. So, if you consider this resistance or this finite slope, what will be getting here it is that one resistance here which is either you can write in the form of conductance or resistance r_o.

The finite slope caused by the Early Voltage Effect can be represented as a small signal output resistance, denoted as r_o. This resistance indicates how much the current changes in response to a change in the collector-emitter voltage, effectively describing the output behavior of the transistor in response to small-signal variations. When modeling circuits including this effect, r_o becomes a critical factor as it reflects the internal behavior of the transistor under specific biases.

Imagine a leaky faucet – the tighter you twist the handle (analogous to increasing V_ce), the less the water drips (decreasing current change). The output resistance r_o represents how effectively the faucet can close off flow. In electronics, understanding how much 'leakage' there is helps in designing circuits.

So, the output resistance R_o, it will be rather R_o = r_o + R_C. So, this represents the complete model of the CE amplifier small signal model of the CE amplifier which is valid for low frequency as well as high frequency. And of course, in the low frequency region ah, then the C_µ and C_π they are affected to be very negligible.

Incorporating the Early Voltage Effect changes the output resistance in the circuit. The total output resistance R_o is now the sum of the small signal output resistance r_o from the Early Effect and the external collector resistance R_C. This means our model captures both the inherent characteristics of the transistor and the added resistances in the circuit. In low-frequency applications, additional capacitances (such as C_µ and C_π) become negligible, simplifying analysis.

Think of the combined output resistance like a team of workers. The output resistance R_o is the full team effort, while r_o is the contribution from one worker (the transistor), and R_C represents additional help from another worker (external resistance). Together, they create a stronger output than any one worker would alone.

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