58.1.7. Cutoff Frequency Calculation

Now, next thing is that we can find the lower and upper cutoff frequency. This is the; this is the exact statement of the problem we have addressed earlier. Now, for our main focus to demonstrate how the bandwidth it will be extended we can probably calculate only the upper cutoff frequency using whatever the information we do have and you may recall the upper cutoff frequency it is considering whatever we do have here.

In this section, we are focusing on defining and calculating the cutoff frequency for an amplifier circuit. The cutoff frequency is a crucial point in the frequency response of the circuit that separates the passband from the stopband. The upper cutoff frequency is significant because it indicates the maximum frequency at which the amplifier maintains its gain before the output starts decreasing. The text mentions how calculations are based on the previously discussed parameters and components.

Imagine you are tuning a radio. The cutoff frequency would be like the limit of frequencies your radio can effectively receive without distortion. Just like how a radio might get fuzzy reception if you tune it to a frequency beyond its limits, an amplifier will lose effectiveness past its cutoff frequency.

So, the value of this upper cutoff frequency can be obtained by considering that 3.1 k multiplied by 10 sorry 100 pF which is 10‒10. And, that gives us I have done the calculation for you. This is coming 513 kHz.

To calculate the upper cutoff frequency, we take the resistance (3.1 kΩ) and multiply it by the capacitance (100 pF). The formula for the cutoff frequency (f) is f = 1/(2πRC). Plugging in the values, we find that the upper cutoff frequency is approximately 513 kHz. This means that at frequencies higher than this threshold, the gain of the amplifier significantly drops, leading to less effective amplification.

Consider a water hose. If the tube is narrow (high resistance), it can only manage a certain amount of water flow efficiently (low capacitance). Past a certain point, if you try to push more water through (high frequencies), the flow starts to reduce dramatically, representing the concept of cutoff frequency in our amplifier.

So in summary what we have circuit performance why should you have the circuit gain is 238 and then the upper cutoff frequencies 513 kHz. Now, the exercise we are going to do it is that we are going to put in this case instead of putting the capacitor here we can probably directly put a CC stage here and rest of the things we will be keeping same.

The section reviews the circuit's performance with a highlighted gain of 238 at an upper cutoff frequency of 513 kHz. It suggests that instead of using a capacitor for filtering, a common collector (CC) stage should be implemented. The CC stage impacts the overall circuit responsiveness and bandwidth, enabling a broader range of frequencies to be amplified effectively.

Think of going to an amusement park. The gain represents the excitement level of rides (238), while the cutoff frequency (513 kHz) indicates the rides you can enjoy without being too dizzy or overwhelmed. Adding the CC stage is like having a bridge to access more rides comfortably, making your visit more enjoyable.

Now to get the overall gain starting from the primary input to primary output first of all this part we already have done and we have seen that it is gain it is if I call A it is gain V1 is 238 and then it is output resistance if I call R which is 3.1 k and then.

When incorporating a CC stage, the overall gain calculation needs to start from the primary input through to the output. The text confirms earlier readings for the first stage's gain (A = 238) and the output resistance (R = 3.1 kΩ). It emphasizes that understanding how each stage affects the gain and resistance is essential for predicting performance outcomes of the multi-stage amplifier.

Picture conducting a relay race. The first runner (representing a stage) has a set speed (gain of 238) and efficiency (3.1 kΩ). Each runner in the relay contributes to the overall performance, with the last runner crossing the finish line representing the total gain of the entire circuit. Analyzing contributions from each stage is crucial to understand the final outcome.

So, in summary we can say that if the original CE amplifier it is having a frequency response like this. So, it is having a gain. So, this is A in dB and this is frequency in Hz in log scale and this one was 513 kHz was the upper cutoff frequency. Now, by adding this CC stage what we have here it is the gain got slightly decreased, but then bandwidth got extended and this bandwidth it is 10 MHz. So, almost 20 times enhancement of the bandwidth.

Summarizing the effects of adding a CC stage, the initial CE amplifier had a limited bandwidth with an upper cutoff frequency of 513 kHz. By integrating the CC stage, the gain may slightly reduce, but the bandwidth improves dramatically to 10 MHz, showcasing a 20 times extension in bandwidth. This enhanced performance is crucial for handling a larger range of frequencies, improving the amplifier's utility in various applications.

Think about upgrading your internet connection. Initially, you could handle a specific number of devices (513 kHz), but after you upgraded your router (adding a CC stage), you can now support many more devices simultaneously without slowing down (extending bandwidth to 10 MHz). This highlights the importance of enhancements in technology that allow us to manage more demands efficiently.

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