41.2.4. Frequency Response from Input to Output

Yeah. So, welcome after the break. So, we are talking about the, in fact, what we got it is the generalized model of CE and CS amplifier here. What it is having here it is the input signal source, having the source resistance of R_s, and then signal coupling capacitor C_1, and then if I consider this is the main amplifier where we do have the input resistance represented by this R_1. And then we do have voltage dependent voltage source, which means that this is the core of the amplifier, then we do have the output resistance R_2. And then C_3 and C_4, they are representing you know either C_π, C_gs or C_gd based on whether the circuit it is CE amplifier or CS amplifier.

This chunk introduces the generalized model of common emitter (CE) and common source (CS) amplifiers. It outlines the key components in the amplifier such as the input signal source, source resistance, coupling capacitor, input resistance, voltage dependent voltage source, output resistance, and capacitors that depend on the type of amplifier being used. These components together define how the amplifier functions and influence the frequency response of the circuit.

Think of the CE and CS amplifiers as a water system. The reservoir (input signal source) holds water (signal), the pipes connected to the reservoir (source resistance) control how much water can flow, and the valves (capacitors and resistances) adjust the flow rate and pressure (gain). Just like any water system, understanding the components and their arrangement is vital to analyzing how effectively the system delivers water to its destination.

So, this particular this capacitor it can be converted into two equivalent capacitance; one is for the input port, the other one is for the output port. And then, the input port part coming out of the C_4 it is what we said is that C_in (1 ‒ A_o) or in this case A_o is equal to v_out/v_in. In fact, if you see here we are putting a ‒ sign here assuming that the polarity of the voltage dependent voltage source, here it is +ve.

In this chunk, we discuss how a coupling capacitor can be separated into two capacitances for input and output ports. The effective input capacitance (C_in) is given by a formula that includes the gain of the amplifier (A_o). The emphasis on the negative sign indicates the phase inversion characteristic common in amplifier circuits. This part of the analysis is critical for calculating the overall frequency response based on the input and output characteristics.

Imagine you’re adjusting the sound level on a speaker system. The speaker (output) needs a certain amount of signal (flow of electricity) from the amplifier (input) to produce sound. The coupling capacitor acts like a faucet controlling how much signal flows to the speaker. If adjusted correctly, you’ll have a clear and robust sound; if not, the sound might be weak or distorted, similar to correctly calculating the capacitance in this circuit.

So, in summary what we have it is at this node we do have the C_in and then at this node we do have the net C_out. Now, to get the frequency response of this circuit namely starting from this point till the primary output what we have it is we do have one network here and then we do have of course, the main amplifier starting from this point to this point and then of course, at this point we do have the C_out.

This section summarizes how the input and output capacitances are determined in the amplifier circuit. It emphasizes the transition from input to output and the significance of understanding how the effective load capacitance influences the overall frequency response. At this point, a more comprehensive view of the network presented is necessary to analyze the frequency response beginning from the input until the output.

Consider a race track where the cars (signals) start and finish at different points. The input capacitance is where the cars begin their race, while the output capacitance determines how they finish. Understanding the changes in speed and performance throughout the race (frequency response) is crucial as it impacts the overall outcome (amplifier performance).

Our first task is to find the frequency response from this point to this point, namely maybe in Laplace domain we can see, and then we can find what is the corresponding transfer function we are getting.

This chunk introduces the essential step of determining the transfer function, which describes how the output of the system relates to its input over a range of frequencies. By employing the Laplace transform, we can analyze the circuit in the frequency domain. This analysis is crucial for engineers as it allows for predictions about how the amplifier will behave under varying input conditions and enables the design of the amplifier for specific frequency responses.

Think of a chef preparing a dish. The transfer function is like the recipe that describes the relationship between the ingredients (input signals) and the final dish (output signal). By understanding how each ingredient affects the taste, the chef can ensure that the final dish meets expectations. Similarly, engineers use transfer functions to predict the behavior of circuits.

So we do have this circuit, we do have R_in, and then C_in, and then R and the C coming in parallel. Now, if you see here to get the frequency response of this circuit namely in Laplace domain.

In this segment, we examine the circuit defined by various resistances and capacitances in series and parallel configurations. Through this approach, we derive the impedance which becomes essential for simplifying the transfer function. This part of the analysis illustrates methods used to derive mathematical relationships that can later be used to evaluate frequency response.

Imagine a plumbing system where various pipes (resistors) are either connected in series or parallel, influencing how water flows (current). Just like you would calculate the overall flow rate based on the size and arrangement of pipes, engineers determine impedance to understand how combinations of resistors and capacitors will impact electrical signals.

So, in summary what we like to say here it is the frequency response of this circuit starting from this point to this point is given by; so, this is the frequency maybe we call it is radian per second and then we do have the gain in dB.

This part synthesizes the overall frequency response observed from the earlier calculations. By plotting the circuit's gain in relation to frequency, one can visualize how the circuit will amplify signals across different frequencies. This plot is crucial for engineers to analyze and design amplifiers effectively.

Visualize a speedometer in a car that shows your speed (gain) at different points in time (frequency). The speedometer allows you to gauge how fast or slow you should go based on the conditions around you. Similarly, the frequency response plot helps engineers see how well an amplifier will perform across a range of signal frequencies.

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