What is the purpose of the second inductor in a T-section LC low pass filter?

[cepheid]

I have a dumb question about "T-section" filters like the one shown on this page:

http://www.radio-electronics.com/in...f-filters/simple-lc-lowpass-filter-design.php

If the output it taken across the two rightmost terminals, then what is the point of the second inductor? It seems to me that if no current flows across the second (rightmost) inductor in the circuit, then it is only the first inductor and the shunt capacitor that really do any filtering, at which point you just have a series LC circuit. What am I missing?

 

[I like Serena]

Wouldn't it matter when you connect a couple of filters next to each other?
In other words, when you have an output impedance?

 

[berkeman]

Wouldn't it matter when you connect a couple of filters next to each other?
In other words, when you have an output impedance?

You are correct. Such filters usually would assume 50 Ohm source and load impedances.

 

[I like Serena]

You are correct. Such filters usually would assume 50 Ohm source and load impedances.

Looks familiar!
Isn't that the standard impedance of any audio equipment?
And aren't interlink audio cables optimized for exactly that impedance?

 

[berkeman]

Looks familiar!
Isn't that the standard impedance of any audio equipment?
And aren't interlink audio cables optimized for exactly that impedance?

That could be, but I don't work with that kind of audio much. I was thinking in terms of RF applications, using components like these:

http://www.minicircuits.com/homepage/homepage.html

.

 

[vk6kro]

50 ohms is very common for RF (Radio Frequency) applications, but low level audio signals are usually at more like 600 ohms to 10000 ohms.

The common "Line" level signals that pass between devices (and marked "line-in" and "line-out") are usually driven at about 100 ohms impedance but the load is about 10000 ohms, so that the majority of the signal appears across the load.

The signal level is nominally 0.316 volts RMS although this depends on the content. This is 0.88 volts peak to peak, but actual levels of up to 2 volts p-p are possible.

 

[jim hardy]

""What am I missing?""


well - what's the purpose of a filter ? to separate a noisy source from a load that wants quiet...?

AHA what is missing from that diagram is the load.
Were there no load there'd be no need to filter

recall maximun power is tranferred when Zload = Zsource
(okay, okay, when they're complex conjugates..)
i think your example should've shown a load of Zo

but i could be wrong...

stellar eye for detail there, Cepheid...

 

[cepheid]

But how would I derive the transfer function (or just the frequency response at least) of the filter? When you say to assume 50-ohm source and load impedances, is that entirely resistive, or is there some reactance? I mean, I realize the answer depends on the application, but I'd like to know how what the filter does.

On a possibly only vaguely related note, I have come across the 50-ohm impedance in connection with coax cables used for transmitting RF signals, but I had alway thought these were on a per metre basis. Is that the case?

Sorry a course on transmission line theory was missing from my education.

 

[I like Serena]

But how would I derive the transfer function (or just the frequency response at least) of the filter? When you say to assume 50-ohm source and load impedances, is that entirely resistive, or is there some reactance? I mean, I realize the answer depends on the application, but I'd like to know how what the filter does.

I don't know how to derive a useful transfer function in this case (with a 50 ohm resistive impedance, the formula is pretty complex and does not yield a simple cut-off frequency).

But the cut-off frequency is part of the specification of the filter (f_c={1 \over \pi \sqrt{LC}} \textrm{Hz}).

On a possibly only vaguely related note, I have come across the 50-ohm impedance in connection with coax cables used for transmitting RF signals, but I had alway thought these were on a per metre basis. Is that the case?

Sorry a course on transmission line theory was missing from my education.

No, a coax cable does not have a 50 ohm impedance on a per metre basis.
It is optimized for a 50 ohm connection.
If you connect the coax cable to equipment with for instance 75 ohm impedance, you'll get reflections and therefore noise.

 

[vk6kro]

But how would I derive the transfer function (or just the frequency response at least) of the filter? When you say to assume 50-ohm source and load impedances, is that entirely resistive, or is there some reactance? I mean, I realize the answer depends on the application, but I'd like to know how what the filter does.

On a possibly only vaguely related note, I have come across the 50-ohm impedance in connection with coax cables used for transmitting RF signals, but I had alway thought these were on a per metre basis. Is that the case?

Sorry a course on transmission line theory was missing from my education.

The behaviour of that circuit varies a lot with the actual components used.

It is quite easy to get resonance effects between the inductors and the capacitor. Generally, the capacitor has to be as large as possible to get a smooth tapering off of the response.

For example, here is the response if the inductors are 1 Henry and the capacitor is 1 μF (with a 50 ohm source and 50 ohm load impedance).
[PLAIN]http://dl.dropbox.com/u/4222062/LCL%20filter.PNG
That peak at 225 Hz would be very undesirable in most applications.

There is a wonderful simulation program available free to anyone who wants it. If you would like to get a copy of this program, I could show you how to use it, off-Forum, so that you could explore such circuits in the future.
It is called LTSPICE 4 and is available from http://www.linear.com/designtools/software/

When you first look at it, it will seem complicated, but you only need about 3 or 4 of the pull-down commands to operate it in normal use.

You can read about Characteristic Impedance here:
http://en.wikipedia.org/wiki/Characteristic_impedance
It is very real and it affects the behaviour of radio signals traveling in it, but it is difficult to measure without appropriate equipment.
Fortunately, it is usually printed on the outer jacket of coaxial cable every metre or so.
Or you can calculate it from the dimensions of the cable.