Understanding RC and LR High/Low Pass Filters & Radio Tuning Circuits

[momomo_mo]

I want to ask the principle behind the RC circuit and LR circuit to become
Hign/Low Pass filter respectively?

How come RC circuit allow high frequencies to pass through but block the low frequencies,however vice versa in the case of LR circuit?

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Also, I want to ask something about the radio tuning circuit,how does it make use of the
resourance principle?

 

[chroot]

Think of it this way:

A capacitor is an open-circuit to DC, and behaves more and more like a short-circuit as applied frequency increases.

An inductor is the opposite: it's a short-circuit to DC, and behaves more and more like an open-circuit as applied frequency increases.

- Warren

 

[leright]

And the reason capacitors act like opens to DC and shorts to high freq. AC and inductors act like opens to high frequency AC and shorts to DC can be explained using Maxwell's third and fourth equations, respectively.

In maxwell's third equation, when there is no ACTUAL current flowing but there is a time varying electric field there is a displacement current. In a capacitor, there is no actual current flowing in a conventional sense, but in AC there is a changing D-field, which means there is a displacement current. In DC, there is no conventional current or displacement current. Displacement is a rather non-intuitive concept and it might require additional reading from you to understand its meaning properly.

In maxwell's fourth equation, it is stated that an EMF is induced in a closed conducting loop in such a way as to drive current in a direction that fights any changes in magnetic flux that occur through the surface defined by the loop. An inductor is simply a bunch of conducting loops laid on top of one another. In AC conditions, a changing current flows through the loops of the inductor, which in turn produces a changing B-field, which in turn produces a changing flux. This results in a current in the direction that produces a flux that fights the changing flux, which would be in the opposite direction of the original current. As frequency gets larger and larger the inductor fights the AC current more and more, and the inductor is modeled more and more closely with an open as current approaches zero. In DC conditions, the inductor acts like a short because there is no change in current, and therefore no change in magnetic flux, and therefore no current in the opposing direction.

 

[leright]

The resonance frequency is the frequency in which the gain of a bandpass filter is at a maximum. The quality of the bandpass filter is the "sharpness" of the resonant peak. The "quality" of the bandpass filter is measured by something called the Q-factor, which is the ratio of the resonant frequency / bandwidth. The reason this ratio is used is because the resonant freq. alone or the bandwith alone tells us nothing about the sharpness of the peak, since a small bandwith could mean a relatively poor sharpness or a relatively good sharpness, depending on the location of the resonant frequency. At a high resonant frequency, a low bandwidth means a high quality, but at a low resonant frequency, a low bandwidth means a relatively low quality.

A simple radio is a bandpass filter with a high quality factor that can be tuned to different resonant frequencies by changing the internal inductance and internal capacitance (this is essentually what you're doing with you adjust your radio dial) of the circuit to pick up various stations and block out other stations. You obviously want a high quality factor (sharp peak), unless you want to listen to a superposition of many different radio frequencies.