33.5.6. Voltage Model

So, that gives us the voltage gain A defined as v_out/v_in = -R_D * g_m. So, this is the first parameter of the voltage amplifier namely the voltage gain.

The voltage gain (A) of an amplifier is defined as the ratio of the output voltage (v_out) to the input voltage (v_in). In this case, the voltage gain is represented by the formula A = -R_D * g_m. Here, R_D is the resistance at the output, and g_m is the transconductance parameter of the amplifier. The negative sign indicates that the output voltage is inverted compared to the input.

Think of a voltage amplifier like a see-saw where one side goes up while the other side goes down. If you push down on one end (input voltage), the other end (output voltage) will rise to a new level, but it may do so inversely, which is why we get the negative sign in the formula.

So, that makes this current 0 and then if you stimulate this output port by say v_x and then if you observe the corresponding current here as i_x. In fact, the current it is only going through this resistance. So, then v_x and the i relationship you will get is basically v_x = R_D * i_x.

To understand the output resistance of the amplifier, you apply a voltage v_x at the output while ensuring that the input is terminated (current is set to zero). The output voltage (v_x) is then directly proportional to the output current (i_x) flowing through the output resistance (R_D). This can be expressed as v_x = R_D * i_x, highlighting the relationship between voltage, current, and resistance.

Imagine trying to push water out of a garden hose. The resistance (R_D) in the hose affects how much water flows out (current). The more you push (voltage), the more water comes out, but the amount that actually comes out is affected by the resistance of the hose.

At the input port if we see and if you see what is the corresponding resistance here... that gives us the expression v_s = (R_1 || R_2).

The input resistance of the amplifier is determined by looking at the resistance at the input port when no current is flowing into it (the gate current is assumed to be zero). We can evaluate the input resistance as the parallel combination of resistances R_1 and R_2. The formula v_s = (R_1 || R_2) shows that the input voltage (v_s) can be expressed as a function of these parallel resistances.

Think of two parallel water slides at a park. When kids slide down, they choose either slide (R_1 or R_2). If both slides are available, more kids can slide down simultaneously, similar to how resistors in parallel share the current, affecting the total input resistance.

Now, as we have given a hint that since the main circuit this current is 0 before we start considering the input capacitance... G = AV/m, therefore relates the transconductance G and the voltage gain A.

In scenarios where the current into the input port is negligible, we can treat the amplifier as a transconductance amplifier. Here, the relationship between the transconductance (G) and the voltage gain (A) is defined mathematically as G = A * V/m, relating the two in terms of output current dependence on input voltage.

Think of a volume control knob on a stereo. When you turn the knob (input voltage), it determines how much loud the stereo plays (output current). The knob adjusts the amplifier's behavior much like the transconductance describes how a small input voltage affects the larger output current.

Now, if we consider the high frequency situation... include the effect of λ, then at the output side it may be having finite conductance.

When analyzing circuits at high frequencies, additional factors such as parasitic capacitances and finite conductance need to be taken into consideration. In this context, as frequency increases, the characteristics of the amplifier change due to these parasitic effects, affecting the overall performance and gain of the output signal.

Consider trying to fill a balloon with air (high frequency) through a tiny straw. As the frequency of filling increases, you encounter resistance not just from the straw size (pulling air through a small opening) but also from the balloon material stretching and pushing back (parasitic capacitances). Both constraints together can limit how quickly the balloon can be filled.

So, as a result the previous analysis it was valid in the mid frequency region... the role of this C and C in the frequency response.

The amplifier has defined cutoff frequencies, namely a lower cutoff and an upper cutoff frequency based on its RC time constants. Understanding these cutoff frequencies is essential as they define the range of frequencies over which the amplifier operates optimally. Any signal or input outside of these frequencies will be attenuated, affecting how the amplifier can be used in practical applications.

Think of a concert speaker system that is tuned to work best within certain frequencies. If you play music that is too bass-heavy (lower cutoff frequency) or too treble-heavy (upper cutoff frequency), the speaker may not sound as good. Just like the speaker has a range in which it performs best, amplifiers have their ranges of optimal frequency response.

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