30.3.4. Cutoff Frequency and Capacitor Calculations

So, as I said that this is what we are from in fact, we already have covered significant part of the numerical examples. And, particularly the operating point and then the and it is stability and then finding performance matrices. And, today we are going to discuss about the design guidelines.

In this section, we begin by discussing the design guidelines for a common emitter amplifier. We focus on ensuring that the amplifier functions correctly by covering operational points, stability, and performance metrics. These guidelines enable the designer to create effective circuits by processing available information such as supply voltage and characteristics of the transistors used.

Think of designing an amplifier like planning a road trip. First, you need to know your starting point (operational point) and your destination (design goals). You also need a stable vehicle (stable design) and a reliable map or GPS (performance metrics) to guide you along the way.

We assume the supply voltage is given to us. Typically, and the supply voltage is given by the customer who requires this circuit. Also, this information may be available particularly whether the BJT is silicon type or germanium BJT.

When designing a common emitter amplifier, we start by gathering essential data such as supply voltage and the type of BJT (Bipolar Junction Transistor). Knowing if the transistor is silicon or germanium helps determine its operating characteristics. We also assume other crucial components are in known ranges, such as bias resistors and capacitor values that are essential for circuit functionality.

Imagine preparing a recipe. You must first check that you have all the necessary ingredients (supply voltage and BJT type). If you don't know what type of flour you have, you might end up with a cake that doesn't rise as expected!

If you see the voltage gain of the common emitter amplifier A, we have discussed that it is magnitude it is g × R .

The voltage gain of a common emitter amplifier (A) can be calculated using the formula A = gm × RC, where gm is the transconductance, and RC is the load resistance. This gain is crucial as it determines how much the input signal will be amplified when it passes through the circuit. The gain cannot exceed the supply voltage, hence it must be designed keeping limits in mind to avoid distortion.

Think of the amplifier like a microphone system. The gain is how much louder your voice becomes after passing through the microphone and speakers. If the gain is set too high and exceeds the speaker's capability, it can distort the sound, making your beautiful singing turn into a garbled mess!

To get meaningful value of this C1, we require additional information about the performance requirement, namely the lower cutoff frequency. If I know that the lower cutoff frequency, we can say that what will be the C1.

Capacitors in the circuit serve to block DC while allowing AC signals to pass. The design involves calculating the value of coupling capacitors based on the desired lower cutoff frequency. The formula for calculating C1 is also linked to the input resistance of the amplifier, ensuring that the required frequency response can be achieved without distortion.

Consider a dance party where certain songs only play during specific times (like the cutoff frequency). You need to arrange speakers (capacitors) that can handle the music well but prevent the slow ballads (DC signals) from crashing the upbeat dance vibes (AC signals)!

Let us see 1 divided by 2 × п × R in cutoff frequency is a say 50 Hz. So, then what may be the value of this C1?

In this example, we set a target lower cutoff frequency of 50 Hz. By substituting this frequency into our formula for the capacitor value, we evaluate the necessity of the component size in the circuit. A suitable capacitor value ensures that the amplifier performs effectively within the desired frequency range.

Think of tuning a radio to catch specific radio waves (frequencies). If you tune correctly (calculate capacitance), you’ll get clear sounds. But if you don't, you’ll either get static or miss the music altogether!

So, we can say that C can also be in the order of µF and likewise, the C2 will follow the same logic for the design based on frequency requirements.

In summary, design guidelines inform us that both coupling capacitors should generally be in the microfarad range (µF) to meet the amplifier’s frequency response requirements. This helps ensure that the amplifier can handle unexpected AC inputs without distortion while providing the expected gain.

Imagine planning a party where you ensure you have enough snacks (capacitors) for your guests (signals). If there are too few, guests might leave hungry (distortion in signals). Having just the right amount means everyone enjoys the party perfectly!

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