Ah, but describing the circuit with math allows easy analysis and
creation without having to assemble a million combinations of parts and
measuring to see the results.
This filter is a low pass with the cutoff frequency selectable in steps.
It uses the same coils for different cutoff frequencies. This filter is
designed to have the same shape and terminal impedances in and out of
the transformers for the selected frequency chosen by the rotary switch.
The transformers give different filter circuit characteristic impedances
for different frequencies, that allows the same inductors to present the
same reactance proportional to the cutoff frequency and the impedance.
The higher impedances between the transformer compared to the speaker
impedance of 4 ohms makes these filters practical. To build at 4 ohms
impedance the capacitors would be at least 2" x 4" x 6" each, but for a
single cutoff frequency only two would be required. The cost of the
impedance changes and frequency changes with constant coil inductances
is that the capacitor value change twice as fast as the frequency
change. So far, good capacitors in the ranges used are cheaper than good
inductors, and it take a simpler switch to change the capacitors and the
transformer taps than to change capacitors and coils. Though switching
would be simpler to change complete filters, just two poles required.
To look at it from a filter designer's viewpoint, the basic filter
designs are often tabulated for an impedance of one ohm and a cutoff
frequency of 1 Hz. Then we can scale them to the frequency and circuit
impedance we desire. To scale them for frequency we multiply inductances
by the frequency change ratio and divide capacitor values by that
frequency change ratio. So to go from 1 Hz to 1 kiloHertz, we multiply
the inductance values by 1000 and divide the capcitors by 1000. Then to
change the impedance we scale again multiplying the inductance values by
the ratio of the impedance change and dividing the capacitors by that
same ratio. So to change from 1 ohm impedance to 5000 ohms, we multiply
the frequency scaled prototype by multiplying each inductance value by
5000 and by dividing each capacitor by 5000. The transformer taps give a
handy sequence of impedances of 8000, 4000, 2000, 1000 and 500 ohms.
These transformere are made for selecting the speaker power level on a
constant voltage 70 volt line in a PA system with many speakers
distributed around the facility where you want more or less sound in
spots. And while the power selected depends entirely on the impedance,
they aren't rate that way. I use those different impedances to allow
scaling to different cutoff frequencies while using the same inductors
because good inductors are much more expensive and less commonly
available than a wide range of capacitors. This technique of varying the
impedance is not a common filter adjusting technique. I may have
invented it. BUT IT WORKS WELL.
There are four poles of switching, one pole for input transformer, one
for the output transformer and two for the shunt capacitor banks. All on
one shaft. The table on the first page shows the transformer impedance,
the cutoff frequency, and the capacitance values required.
Fundamentally, a low pass L/C filter takes advantage of the fact that
the reactance of an inductor rises as we go up and frequency and that
the reactance of a capacitor goes down as we go up in frequency. So the
series impedance rises with frequency and the shunt impedance goes down
with frequency so the voltage divider changes more rapidly than either
alone to make a more effective low pass filter than either part alone.
Adding more stages of each as in this filter makes the cutoff that much
more rapid.
There are literally dozens of different designs of low pass filters with
differing ratios between L and C to give different cutoff shapes that
have been derived over a century of higher math applications. There are
often good reasons for choosing one over another, such as the slope of
the cutoff, the 2nd and 3rd harmonic attenuation, the ultimate harmonic
attenuation, the transient (e.g. ringing or lack of ringing) response,
and for power filters, the circulating current in the parts.
With more complex math it is the standard technique to derive bandpass,
high pass, and band stop filters from the same 1 Hz 1 ohm low pass
filter prototypes from sub sonic through microwaves made of coils and
capacitors, or vibrating metal bits (as in a mechanical filter),
vibrating quartz or ceramic, or chunks of waveguide suitably modified by
added metal or plastic bits as well a active filters either with op amps
or by digital means.
73, Jerry, K0CQ
On 1/28/2011 1:09 AM, Richards wrote:
> Please forgive my novice inquiry, I'm only part way through the ARRL
> Understanding Basic Electronics book....and I hate mathematics, so it is
> slow going.
>
> Trying to understand the schematic in your article, and looking at all
> those capacitors… Am I to understand this is a variable filter, meaning
> it covers a variable range? I make out two transformers, but I don't
> see anything that might constitute a variable control, so I'm assuming
> this is a single level filter – i.e., one that I can put in the audio
> circuit, or take out, but that's all I can do – you cannot shape or
> very it in any way. It is just that all those little capacitors lined
> up at the bottom of the schematic sort of suggest you are tapping at
> different levels, but I don't see any way to control that.
>
> Is this correct? Thank you for your consideration.
>
> Happy Trails.
> ======================= Richards / K8JHR =========================
>
> On 1/28/2011 12:25 AM, Dr. Gerald N. Johnson wrote:
>> I use an external speaker passive low pass filter to tone down high
>> frequency howling in my receiver audio
>
>
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