# Unity gain in lowpass STC circuit

• Engineering
• gambit1414
In summary, the conversation discusses finding the frequency at which the gain becomes 0dB for a low pass Single Time Constant circuit. The solution manual states that since the gain falls off at a rate of -20dB/dec starting at the 3dB frequency of 10^6, it will reach 0dB in 2 decades (a factor of 100). The unity gain frequency is then calculated to be 10^8. The individual is unsure about how the gain will reach 0dB in 2 decades, as the graph of a low pass STC circuit starts at 0dB and then decreases at -20dB/dec. They also mention that the dc gain is given as 100 V/V = 40
gambit1414
One of the question asks to find the frequency at which the gain becomes 0dB for a low pass Single Time Constant circuit. In the solution manual after finding the 3dB frequency = 10^6, it states that since the gain falls off at a rate of -20dB/dec (see attatchment for graph) starting at w0(Omega-knot) , which is 10^6, the gain will reach 0dB in 2 decades (a factor of 100), therefore unity gain frequency = (10^6)(10^2)= 10^8. Now i don't understand how the gain will reach 0dB in 2 decades, because if you look at the graph of a low pass stc circuit it starts off at 0dB then falls by -20dB/dec. Am i reading the log scale graphs incorrectly? Please clarify. Thank You.

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Sorry, the dc gain (K) is also given which is 100 V/V = 40dB, so it seems like the gain should be 40dB until w=w0 (omega = omega-knot), then the gain starts to attenuate at -20dB/dec. I'm not really good at reading the log graphs so does this mean depending on what your dc gain value is, it will start there and then start decreasing at -20dB/dec after 3dB frequency? Thanks Again.

Thank you for your question. I can understand why you may be confused by the solution provided in the manual. Let me try to explain it in more detail.

In a lowpass STC (single time constant) circuit, the gain starts off at 0dB (unity gain) and then decreases as the frequency increases. The rate at which the gain decreases is called the "roll-off rate" and is typically measured in decibels per decade (dB/dec). This means that for every decade increase in frequency, the gain decreases by the specified amount.

In your case, the roll-off rate is -20dB/dec, which means that for every decade increase in frequency, the gain decreases by 20dB. So, at the 3dB frequency (10^6), the gain has decreased by 20dB. This means that at the next decade (10^7), the gain will decrease by another 20dB, making it -40dB. At the next decade (10^8), the gain will decrease by another 20dB, making it -60dB. And so on.

Now, if we want to find the frequency at which the gain becomes 0dB, we need to find the point where the gain reaches unity gain again (0dB). Since the roll-off rate is -20dB/dec, it will take 2 decades (a factor of 100) for the gain to decrease from -40dB to 0dB. This means that the frequency at which the gain becomes 0dB will be 2 decades (a factor of 100) higher than the 3dB frequency, which is why the solution manual states that the unity gain frequency is (10^6)(10^2) = 10^8.

I hope this explanation helps to clarify the concept for you. If you have any further questions, please let me know.

## 1. What is unity gain in a lowpass STC circuit?

Unity gain refers to the condition in which the output voltage of a circuit is equal to the input voltage. In a lowpass STC (series-resistance, capacitor) circuit, unity gain occurs at the cutoff frequency, where the magnitude of the output voltage is equal to the magnitude of the input voltage.

## 2. How is unity gain achieved in a lowpass STC circuit?

Unity gain can be achieved in a lowpass STC circuit by selecting the appropriate values for the resistor and capacitor. The resistor should be chosen to have the same magnitude as the reactance of the capacitor at the cutoff frequency. This will result in a voltage divider effect, causing the output voltage to be equal to the input voltage.

## 3. Why is unity gain important in a lowpass STC circuit?

Unity gain is important in a lowpass STC circuit because it allows for a flat frequency response at the cutoff frequency. This means that signals with frequencies below the cutoff will pass through the circuit with minimal attenuation, while signals with frequencies above the cutoff will be attenuated. This is useful in filtering out high frequency noise from a signal.

## 4. What happens if unity gain is not achieved in a lowpass STC circuit?

If unity gain is not achieved in a lowpass STC circuit, the output voltage will be either higher or lower than the input voltage. This will result in a non-flat frequency response, where some frequencies will be attenuated more than others. This can lead to distorted or altered signals at the output of the circuit.

## 5. Can unity gain be achieved in other types of circuits?

Yes, unity gain can be achieved in other types of circuits such as highpass STC circuits, op-amp circuits, and active filters. In these circuits, the values of the components will need to be carefully selected to achieve the desired unity gain condition.

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