Circuits and low pass filters

In summary, to calculate the 3dB frequency, use the formula f = 1 / (2piRC) and plot the impedance of the series circuit at different frequencies. For a high pass filter, the circuit diagram will have the capacitor in series and the resistor in parallel.
  • #1
Monsu
38
1
You are given a low pass filter of 50nF and a resistor of 100 KOhm.
a) Draw the circuit diagram;
b) Calculate the 3dB frequency;
c) Calculate the impedance of the series circuit of R and C and draw it in the complex plane at
about 2 decades around the 3dB point and at the 3dB point.
d) Draw the circuit diagram for a high pass filter with same components.



I am asked to calculate the 3db freq, right? is this the right formula f = 1 / (2piRC) ?
and afterwards calc the impedance z = R + jXc where Xc = 1 / (2pifC) ?
and then getting the decades, say our freq was 31.8Hz , 2 decades below would b 0.318? 2 decades above would b 3180?
then we should use those values of f to determine the Xc at those frequencies, and then find z at each of these frequencies?
then we plot a graph showing all the z's?


pls smne help me coz I'm totally confused!
thanks in advance! :smile:
 
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  • #2
Yes, the formula you mentioned above is correct for calculating the 3dB frequency. You can use it to calculate the impedance of the series circuit at different frequencies. You should plot a graph showing the impedance at each frequency. For a high pass filter, the circuit diagram will be similar to the low pass filter with the capacitor in series and the resistor in parallel.
 
  • #3



a) The circuit diagram for a low pass filter with a 50nF capacitor and a 100 KOhm resistor would look like this:

[Image: Low Pass Filter Diagram]

b) To calculate the 3dB frequency, we can use the formula f = 1 / (2piRC). Plugging in the values of 50nF for C and 100 KOhm for R, we get:

f = 1 / (2 * pi * 100000 * 0.00000005) = 318.3 Hz

c) The impedance of the series circuit of R and C can be calculated using the formula z = R + jXc, where Xc = 1 / (2pi*f*C). At the 3dB frequency of 318.3 Hz, the impedance would be:

z = 100000 + j * (1 / (2 * pi * 318.3 * 0.00000005)) = 100000 + j * 99.4 Ohms

To plot the impedance in the complex plane, we can use the values of f calculated in part (b) to determine the Xc at 2 decades below and above the 3dB point. This would give us the following values:

At 0.318 Hz: Xc = 1 / (2 * pi * 0.318 * 0.00000005) = 3.16 MOhms
At 3180 Hz: Xc = 1 / (2 * pi * 3180 * 0.00000005) = 3.16 KOhms

Plotting these values on the complex plane, we get the following graph:

[Image: Impedance Graph]

d) To create a high pass filter with the same components, we can simply switch the positions of the capacitor and resistor in the circuit. The circuit diagram would look like this:

[Image: High Pass Filter Diagram]

The 3dB frequency and impedance calculations for the high pass filter would be the same as the low pass filter, except the roles of R and C would be reversed.
 

1. What is a circuit and how does it work?

A circuit is a path that allows electricity to flow from a source (such as a battery) to a load (such as a light bulb). It typically consists of components such as resistors, capacitors, and inductors, which regulate the flow of electricity.

2. What is a low pass filter and what is its purpose?

A low pass filter is an electronic circuit that allows low frequency signals to pass through while attenuating (weakening) high frequency signals. Its purpose is to filter out unwanted high frequency noise from a signal.

3. How does a low pass filter work?

A low pass filter consists of a resistor and a capacitor in series. The resistor limits the current flow, while the capacitor stores and releases energy. As the frequency of the input signal increases, the impedance (resistance) of the capacitor decreases, allowing more current to flow through and filtering out high frequency signals.

4. What are some applications of low pass filters?

Low pass filters are commonly used in audio systems to remove high frequency noise from music or speech signals. They are also used in power supplies to filter out high frequency noise from the main power source. In addition, they can be used in electronic filters to separate different frequency components of a signal.

5. What are the differences between active and passive low pass filters?

Active low pass filters use active components such as transistors or op-amps to amplify or attenuate the signal, while passive low pass filters use only passive components such as resistors, capacitors, and inductors. Active filters can provide a steeper roll-off (greater attenuation of high frequencies) and have a lower output impedance, but they require a power source. Passive filters are simpler and do not require a power source, but may not provide as much attenuation of high frequencies.

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