27.1.1. Common Emitter Amplifier (Contd.) (Part B)

So, welcome back after the short break. So, where we are discussing? We are talking about the small signal equivalent circuit and then we are trying to find the corresponding gain of the circuit.

In this section, we reintroduce the concept of a small signal equivalent circuit, which is crucial for analyzing the behavior of amplifiers like the common emitter amplifier. This circuit simplifies the complex nonlinear behavior of transistors around a specific operating point into a linear model, allowing us to calculate important parameters like gain.

Think of it like tuning a musical instrument. To get the perfect sound (or gain, in our circuit), we first identify the specific note we are trying to play (the operating point) and then adjust our strings (the circuit parameters) to achieve the right pitch (the gain).

The output voltage as I said that output voltage, it is this one. So, v = – g × R × v. Now, this v of course, it is function of v, but we need to find what is the exact expression of that.

The output voltage (v) of the common emitter amplifier can be described by the formula v = – g × R × v. Here, 'g' refers to the transconductance of the transistor, and 'R' is the resistance in the circuit. This equation shows us how the output voltage is dependent on the input voltage, indicating that it is amplified by a specific factor involving these parameters.

Imagine turning the volume knob on a radio; the input voltage is like the signal coming in, and the output voltage is the sound we hear, amplified by the radio's components. The gain is how much louder we can make the sound.

However, unfortunately, this is also desensitizing this circuit against input signal and as a result it is making the gain much smaller than whatever the original gain of the CE amplifier potentially can provide.

Inserting an emitter resistor (R_E) into the circuit aims to stabilize the operation point against variations in the transistor's beta (β), but it has the side effect of reducing the overall gain of the amplifier. This occurs because the resistor provides a path for the input signal to lose some of its amplitude, similar to a leakage in a water pipe causing reduced pressure downstream.

Think about trying to fill a balloon with air. If there's a small hole in the balloon (the emitter resistor), some of the air escapes (signal amplitude decreases), making it harder to inflate the balloon fully (achieve maximum gain).

We do have two more important parameters namely input resistance and output resistance of the model.

In amplifier circuits, input and output resistance are critical factors that affect how the amplifier interacts with other components. The input resistance defines how much the amplifier will draw from the input signal source, while the output resistance affects how the amplifier loads the connected output devices.

Consider a blender. The input resistance is how much force the ingredients have to exert against the blades when first added. If the blender’s output resistance is too high (like a thick material), it might struggle to blend smoothly (not transfer the signal effectively).

While we will be talking about input resistance, we may consider this R, but while here we are deriving this voltage gain A, we have ignored!

While analyzing the amplifier's performance, especially when calculating gain, certain resistances in the circuit (like R_B) might be neglected for simplification. This is often practical in theoretical calculations, as they don't significantly impact the primary function being evaluated, allowing for clearer focus on the key elements.

It’s like cooking a recipe; while measuring might be critical for the main ingredients, minor spices could be ignored during early tests to focus on the fundamental flavors before fine-tuning.

While we will be doing this similar kind of exercise, we need to find as I said that we need to find what will be the output resistance R of this voltage amplifier.

The output resistance is found by applying a known voltage at the output and measuring the resulting current. The formula resulting from this measurement tells us how the amplifier will behave when connected to subsequent stages or loads, crucial for overall system performance.

Think about a speaker system; the output resistance can be compared to how much power a speaker can deliver to the sound space. If the output resistance is too high, the speaker won’t drive the sound through the room effectively.

So, if we make this voltage whatever the emitter voltage; if we make 0, then we can then force this v to be equal to v.

By introducing a capacitor in parallel with the emitter resistor, we can effectively remove the resistor's influence at high frequencies while maintaining stability at low frequencies. This allows us to achieve a higher gain without compromising the stability of the amplifier's operating point.

Imagine a dam controlling water flow; at some times, water can be released freely (high frequency conditions) when a flood (input signal) occurs, but at other times, it must be held back (low frequency stability). The capacitor acts like a valve that opens and closes quickly based on the needs.

So, we need to discuss some of the numerical problems, but today we are running short of time probably in the next class we will talk about numerical problems from both angles the design wise as well as analysis wise.

As we wrap up this section, it's vital to apply what we've learned through practical numerical problems to cement our understanding of both circuit design and the performance analysis of the common emitter amplifier.

It’s akin to practicing math problems after learning new concepts in class. Each problem helps clarify the theory while also preparing you for real-world scenarios where these applications are necessary.

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