WHAT ARE LOW PASS FILTERS?
Consider the circuit shown in Figure 2.32 . Note similarities to the RC circuit that we used to first understand the effects of a capacitor. The difference is that now we are going to apply an AC signal to the input rather than the step input we applied before.
This circuit is known as a low-pass fi lter, and all you really need to know to understand it is the voltage divider rule and how a capacitor reacts to frequency. If this were a simple voltage divider, you could figure out, based on the ratio of the resistors, how much voltage would appear at the output.
Remember that the cap is like a resistor that depends on frequency and try to extrapolate what will happen as frequency sweeps from zero to infinity. At low frequencies the cap doesn’t pass much current, so the signal isn’t affected much.
As frequency increases, the cap will pass more and more current, shorting the output of the resistor to ground and dividing the output voltage to smaller and smaller levels. There is a magic point at which the output is half the input.
It is when the frequency equals 1/RC. You might have noticed that this is the inverse of the time constant that we used earlier when we first looked at caps. Kinda cool when it all comes together, isn’t it? This is known as a low-pass filter because it passes low frequencies while reducing or attenuating high frequencies. You can make a low-pass filter with an inductor and resistor, too.
Given that the inductor behaves in a way that is opposite of a capacitor, can you imagine what that might look like? Have a look at Figure 2.33 .
That’s right; you swap the position of the components. That’s because the inductor (being the opposite of a cap) passes the lower frequencies and blocks the higher frequencies. It performs the same function as the low-pass RC circuit but in a slightly different manner. You still have a voltage-divider circuit, but instead of the resistor-to-ground changing, the input resistor is changing.
At low frequencies the inductor is a short, making the ground resistor of little effect. As frequencies increase, the inductor chokes 28 off the current, reacting in a way that makes the input element of the voltage divider seem like an increasingly large resistance.
This in turn makes the resistor to ground have a much bigger say in the ratio of the voltage-divider circuit. To summarize, in the low-pass fi lter circuits, as the frequencies sweep from low to high, the cap starts out as an open and moves to a short while the inductor starts out as a short and becomes an open.
By positioning these components in opposite locations in the voltage-divider circuit, you create the same filtering effect. The ratio of the voltage divider in both types of fi lters decreases the output voltage as frequencies increase.
All this lets the low frequencies pass and blocks the high frequencies. Now, what do you suspect might happen if we swap the position of the components in these circuits?
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