Parallel RL Circuits: Uses & Impedance Matching

[davenn]

This query comes from not being able to answer some one else's query
it show's I have been away from textbooks and classrooms way too long ( see my signature )
I have forgotten my basics

These RL circuits

Now I realize A and B are just the same with the RL rotated
and following that C would be the same as B with the load inserted below the RL
For C ... What difference is there if the load is say
1) antenna
2) some other circuit on a separate module ( possibly/probably capacitively coupled)

or if circuit B and the load was parallel across the source and the RL network ?

Bouncing around a number of www sites infers that the parallel RL is used as a form impedance matching
between the source and load ?
I cannot find specific comments for another use ... is there one ?
I was considering a filter ...

with ref to ...
http://amrita.vlab.co.in/?sub=1&brch=75&sim=322&cnt=1
Theory:
With an ac signal applied to it, the parallel RL circuit shown below offers significant impedance to the flow of current. This impedance will

change with frequency, since that helps determine XL, but for any given frequency, it will not change over time.
Then gets into a mass of complex impedance calc's as most sites do

one place seen was in an FM phase modulator circuit ...

I haven't played with phase modulation circuits ... so not too sure of the process therea little help in understanding please

cheers
Dave

 

[jim hardy]

Then gets into a mass of complex impedance calc's as most sites do

Seems to me that "mass of calc's" was unnecessary.

Why they let it get more complex than this, their own starting point,

is a mystery to me.

You'll remember this from 1960s...

Every new scientist must learn early that it is never good taste to designate the sum of two quantities in the form:

Anyone who has made a study of advanced mathematics is aware that:

Therefore eq. (1) can be expressed more scientifically as:

This may be further simplified by use of the relations:

Equation (2) may therefore be rewritten as:

At this point it should be obvious that eq. (3) is much clearer and more easily understood than eq. (1). Other methods of a similar nature could be used to clarify eq. (1), but these are easily divined once the reader grasps the underlying principles.

https://totient.wordpress.com/2008/03/19/a-funny-derivation/

 

[davenn]

@jim hardy haha ... why do people do that to us poor non-mathematical people
and 1+1=2 also depends on who you are ... a statistician, mathematician, an engineer or a philosopher

But we digress
Any help with understanding what this RL circuit is doing ?Dave

 

[jim hardy]

Any help with understanding what this RL circuit is doing ?

Circuit C ?

I'd treat it as a voltage divider.
Vout = Vin X (Rload)/(Rload + (R1 parallel L1))

and plot Vout/Vin for frequencies where X_L<< either resistor to X_L>> either resistor.

At DC, Vout = Vin
and when X_L>> either resistor, Vout = Vin X Rload/(R1+Rload)
If one sets Rload = K*R1
there's some frequency where X_L = R1, ω = R1/L1, so one could derive a family of curves of attenuation vs frequency.for various K's

Sound plausible?

old jim