37.1.3. Small Signal Equivalent Circuit

So, say to start with we do have common source amplifier and the circuit is given here. The circuit is given here for your reference and if you see here we do have the main part main amplifier here and then, we are feeding the signal through this capacitor called say C . At the output we are observing the signal after removing the DC part through the C . In addition to that, it may have some capacitive load coming from the next subsequent circuit. So, let you call this is C .

The small signal equivalent circuit is a simplified representation of an amplifier circuit, in which we consider only the AC signals while ignoring any DC components. In this example, we focus on a common source amplifier, which is typically used in various electronic applications. The input signal is first fed to the amplifier through a capacitor (denoted as C), which blocks any DC voltage and allows only AC signals to pass. The output signal is also affected by a capacitor (denoted as C) that may come from the next stage of the circuit. These capacitors play a crucial role in coupling signals across different stages in an amplifier.

Imagine you are listening to music on your phone but want to prevent your phone from charging while listening. The capacitor acts like a gatekeeper—allowing the music (AC signals) to flow through while blocking any charging currents (DC signals). This ensures that the sound remains unaffected by any direct current that might distort the audio.

What we obtained in our previous discussion we say that at the middle, at the middle we got the main amplifier circuit and here of course, it is the small signal equivalent circuit; where, V it is V node, it is AC ground and the transistor it is getting replaced by its small signal model which is voltage dependent current source called i . And its expression it is given by transconductance g × v . v is the voltage appearing across gate to source of the transistor. So, this is the v .

In this part, we transition from the actual amplifier to its small signal equivalent model. We replace the transistor in our circuit with its small signal representation, which acts as a voltage dependent current source. The output current (denoted as i) generated by this model is proportional to the transconductance (g) and the voltage (v) across the gate-source terminals of the transistor. This simplification allows us to analyze the small signal behavior without dealing with the complexities of the actual device.

Think of this concept like a dimmer switch for lights. The amount of light (output current) depends on how much you turn the dimmer (gate-source voltage). This relationship allows you to control the light effectively, similar to how we control the output current based on the small signal equivalent parameters of the transistor.

So, based on this v, we are getting this current and then that current it is flowing through this R and then, of course, we are getting a voltage here. Note that still this is not on equivalent, but it can be easily converted into Thevenin equivalent, namely we can make the amplifier which is having a gain of ‒ g × R .

Here, we observe that the current generated from the voltage across the gate-source terminals flows through a resistor (R), producing an output voltage. The concept of Thevenin's theorem is introduced, which allows us to represent complex circuits with simpler equivalent circuits. In this case, we can replace our amplifier circuit with a Thevenin equivalent that has a specific gain determined by the negative product of the transconductance (g) and resistor (R). This simplification is critical for understanding the behavior of our circuit in analysis and design.

Imagine you are studying a multi-layer cake that looks very complicated. But if you focus on one layer at a time and describe it simply (like Thevenin's theorem), you can grasp the overall structure more easily. The Thevenin equivalent allows engineers to work with complex circuits in a simpler, manageable manner, understanding their behavior layer by layer.

Likewise, input side again this two part these two resistors you can translate into equivalent resistance here, which it will be R ⫽ R . So, what we can see here that C ; this C . So, this is the C and then, this R which is R ⫽ R , they are forming one C-R circuit.

In the small signal equivalent circuit, we identify the resistors and capacitors that contribute to the overall equivalent resistance and capacitance. On the input side, two resistors are combined to yield an equivalent resistance, while on the output side, certain resistors and capacitors combine to form a C-R circuit. This combination of components allows us to analyze how the circuit responds to changes in frequency, as the arrangement of capacitors and resistors influences the amplifier's frequency response characteristics.

Think of two different paths leading to the same destination. Each path (resistor) affects how quickly you can get there (impedance) depending on whether you take the faster route (lower resistance) or a slower more scenic route (higher resistance). Similarly, capacitors in the circuit influence how signals are combined and processed, affecting the amplifier's performance.

This the C-R circuit is getting formed here and then, output resistance which is R and then this C along with this C coming in series, they are these two are farming another circuit which is of course, this is R-C circuit. And this capacitor value, it is it is basically C ⫽ C and its expression it is sorry, this is 2 L in series; this is in series.

In this section, we recognize that the combination of capacitors and resistors forms specific types of filters recognized in the frequency domain. We discuss the formation of both C-R and R-C circuits, which can be analyzed for their effects on the gain and frequency response of the amplifier. When capacitors are arranged in series, their values combine in specific expressions, affecting how they will influence the overall response of the amplifier in various frequency ranges.

Consider a swimming pool with different depths. If the presence of children (capacitors) jumping into the shallow part (C-R circuit) or deep end (R-C circuit) creates waves, those waves represent frequency response. Depending on how deep (the capacitance values) and how wide (the resistance values) the pool is, the behavior of the waves (signal response) changes significantly in amplitude and frequency characteristics, just like how an amplifier responds to input signals.

So, what we are getting here? It is that the amplifier, it can be translated into that unified model which we have discussed just now, before the short break; where, it is having C , then R and then across this R the voltage it is v and that v , it is generating a voltage in which is whatever ‒ g × R time times this v.

After forming the equivalent circuits, we summarize how this information can be applied in the design and analysis of amplifiers. The amplifier can be represented in a unified model which indicates how the capacitors, resistors, and voltage contribute to the overall behavior of the amplifier. By understanding these relationships, we can tweak various parameters to achieve desired performance in terms of gain, cutoff frequencies, and other specifications.

Imagine a DJ at a music festival, mixing different tracks (parameters of the amplifier) to get the perfect sound (amplifier output). Each adjustment (resistor and capacitor) changes how the music (signal) is heard by the audience. By optimizing these settings, the DJ ensures that everyone enjoys the best listening experience, just as engineers fine-tune amplifiers for optimal performance.

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