Red Wave Radio

Quote:

>LC circuits scale nicely with frequency. To move from 40 to 30 meters,
>scale the inductance and capacitance by sqrt(30/40).

??

I would try scaling the inductance and capacitance inversely proportional
to frequency.  For example, in going from 7MHz to 10 MHz, a 100 pF
capacitor would be scaled to 70 pF, while the resonating inductor would
scale from 5.17 uH to 3.62 uH.  You usually scale all the inductors
and capacitors, including the coupling/shunt elements.

For casual use, this is probably close enough.  

However, stuff like input and output impedances often vary
with frequency unless feedback is used to control them.  Thus,
the networks may have to changed to accommodate the new impedances.
Also, when you scale something from 7 MHz to 3.5 MHz, you might
not want to scale the bandwidth.  A high performance CW only filter
might cover just 7.0 to 7.05 MHz (or even less of the band).  Scaled,
only 25 kHz of the 3.5 MHz band would be covered, which would probably
be inadequate.  Sacrificing the part of the 40 meter band you never
listen to is an effective way of improving receiver performance.  
Remember, all those broadcast stations combine to produce a really big
signal (calculate the PEP of all those tones).

Zack Lau  KH6CP/1

                                  Operating Interests: 10 GHz CW/SSB/FM
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Phone (if you really have to): 203-666-1541

Probably, but the formula is F=1/(2*pi*sqrt(LC) so scaling by the
sqrt of the frequency ratio gives a better approximation. In this
case, moving from 40 to 30 meters requires a 0.86 scale factor.

Quote:>However, stuff like input and output impedances often vary
>with frequency unless feedback is used to control them.  Thus,
>the networks may have to changed to accommodate the new impedances.

If you move both reactances equally, the impedance of the network
should remain the same at the new frequency as the unscaled network's
impedance at the old frequency. If you only scale one of the reactances,
the network impedance will change with the frequency shift.

Gary
--
Gary Coffman KE4ZV          |    You make it,     | gatech!wa4mei!ke4zv!gary
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So, to double F you need to halve sqrt(LC), according to the
formula.

Or, squaring both sides, F^2 is proportional to 1/LC

Note that if you make 1/L proportional to F and 1/C proportional
to F you get an *exact* scaling. Pretty convenient, IMO.

It seems that Gary has botched the math.  Fortunately, I have
lots of patience. :-).

Quote:

>>However, stuff like input and output impedances often vary
>>with frequency unless feedback is used to control them.  Thus,
>>the networks may have to changed to accommodate the new impedances.

>If you move both reactances equally, the impedance of the network
>should remain the same at the new frequency as the unscaled network's
>impedance at the old frequency. If you only scale one of the reactances,
>the network impedance will change with the frequency shift.

Sorry about that, I was writing about the impedances of the devices
being matched by the network, and not the network itself.  This is
the great thing about MMIC or monolithic microwave integrated circuits
with 50 ohm input and output impedances.  Your typical active mixer chip
isn't as well behaved.

I must say that associating terms like "feedback" or "control"
to passive LC circuits is a bit unusual.  You working on something
really ***?

Zack Lau  KH6CP/1

                                  Operating Interests: 10 GHz CW/SSB/FM
US Mail: c/o ARRL Lab                                  80/40/20 CW
        225 Main Street           Station capability: QRP, 1.8 MHz to 10 GHz
        Newington CT  06111                    modes: CW/SSB/FM/packet
                                                      amtor/baudot
Phone (if you really have to): 203-666-1541

Yes, and that requires scaling each of L and C by 1/1.4142135..
or 1/sqrt(2).

Quote:>Or, squaring both sides, F^2 is proportional to 1/LC

Yes, or written another way to express the ratio: F1^2/F2^2=(L2*C2)/(L1*C1)

Quote:>Note that if you make 1/L proportional to F and 1/C proportional
>to F you get an *exact* scaling. Pretty convenient, IMO.

Yes, but the proportionality isn't a linear relationship, as you noted
above, it's actually F^2 that's proportional to 1/LC. Don't confuse
equal reactances with equal inductances and capacitances.

Quote:>It seems that Gary has botched the math.  Fortunately, I have
>lots of patience. :-).

Fortunately I have equal patience. I don't think I botched the math,
you botched the concepts by making the leap from F^2 proportional to
1/LC to F being proportional to 1/L and 1/C. That's true, but it's
only true for the combination if you scale *one* of L or C, not when
you scale both at the same time. Then you must consider the squared
terms and the scaling factor becomes F1^2/F2^2. Hmmm, I did botch
the math, F1^2/F2^2 isn't the same as sqrt(F1/F2). But it's not the
same as simply scaling both L and C by F1/F2 either as you propose.

Quote:>>>However, stuff like input and output impedances often vary
>>>with frequency unless feedback is used to control them.  Thus,
>>>the networks may have to changed to accommodate the new impedances.

>>If you move both reactances equally, the impedance of the network
>>should remain the same at the new frequency as the unscaled network's
>>impedance at the old frequency. If you only scale one of the reactances,
>>the network impedance will change with the frequency shift.

>Sorry about that, I was writing about the impedances of the devices
>being matched by the network, and not the network itself.  This is
>the great thing about MMIC or monolithic microwave integrated circuits
>with 50 ohm input and output impedances.  Your typical active mixer chip
>isn't as well behaved.

Ok.

Quote:>I must say that associating terms like "feedback" or "control"
>to passive LC circuits is a bit unusual.  You working on something
>really ***?

Not me, you introduced the subject, note the nesting level. I just
commented that you can keep the passive network's impedance transform
constant by scaling both L and C together. If that's not your design
goal, don't do it that way.

Gary
--
Gary Coffman KE4ZV          |    You make it,     | gatech!wa4mei!ke4zv!gary
Destructive Testing Systems |    we break it.     | uunet!rsiatl!ke4zv!gary
534 Shannon Way             |    Guaranteed!      | emory!kd4nc!ke4zv!gary
Lawrenceville, GA 30244     |                     |