Filter: First Order Low Pass Filter

In this week, we are going to talk about filter in terms of circuit theory. The roles of filter mainly are change frequencies or phase component of the input signal. Normally, it use to emphasize the signal with interested frequency. So, filter are the device that play with the spectrum. For example, here, we have f1 and f2 frequency and if we have filter which have the math model like in the figure. If this signal pass through the filter the f2 will be attenuate.

To describe the filter, the transfer function in Laplace domain is used. The transfer function mean the ratio of the input and output signal in complex frequency domain. This transfer function can explain 2 characteristics of filter. The first one is the frequency response or sometimes it call magnitude response. Trivially, it tells the corresponding between magnitude and frequency of the signal. And the another one is the phase response, it tells the corresponding between the phase and frequency.

For example here, if we have the RLC circuit. We can use the s domain with circuit analysis and the we will get the transfer function of this circuit. From this transfer function, we will easily get the frequency response and the phase response by following. Therefore, we can use MATLAB or others program language to plot this function. Here, we use the MATLAB. The result is here.

It can easily see from the graph that this circuit perform themselves as the bandpass filter which means it can select the interval for the pass band of frequency.

Now we are going to look at the low pass filter. Trivially, this means it will attenuate the high frequency and let the low frequency pass. This leads to this question, what is mean high and low. To determine high and low it will have something call cut off frequency. If the input signal have frequency more than the cut off frequency it will attenuate while if its less than, it will let it pass. So. to design the low pass filter, the transfer function is analyze using the inverting configuration and the cut off frequency will give you at 1/RC. For the example here, we design for cut off frequency equal to 1 KHz. So, we get the component as follow. The transfer function is obtain with the designed component. The frequency and phase is shown as follow.

To remind that, the frequency here is the normalize frequency which is the input frequency divide by cut off frequency. For the gain analysis, it can realize by follow.

Before, we go to the experiment, let simulate with the LTspice and use the AC analysis to perform frequency sweeping.

Now, the circuit is verify. Let’s do the experiment. Because I do not have the exact resistor, so I will use more than one resistor. It is not a good practice but it can acceptable. Here, I am using the LM358 as the op amp which different in the simulation.

While you do the experiment, you cannot automatic sweep the frequency. So, you need to done manually and collect the data. Finally, we are going to plot these data.

Thanks for reading.