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Anthony Fremont March 19th 07 04:23 PM

LC Oscillator Questions
 
Pictures available in ABSE

The top trace (yellow) is taken between C4 and R2. The bottom trace (cyan)
is taken at the base of the transistor. There is a switchercad file, but
the simulation will show allot of distortion that really isn't present in
the prototype circuit, because of lots of circuit capactance I suspect. R1
was something I was playing with to try and tame the voltage across L1/C3
being applied to the base.


Hello all,

I was tinkering with this LC oscillator (Colpitts/Clapp) this weekend. I
arrived at the values of C1 and C2 empirically after starting with a crystal
oscillator circuit. The values in the original circuit created a horrid
waveform that looked allot like the simulation. After much tinkering around
and simulating, I come to the conclusion that getting a perfect waveform is
nearly impossible, especially with big swing. It seems that the transistor
likes to take a bite out of the right half of the peak of the wave.

What is the secret to beautiful waveforms? Do I need another LC resonator
on the output to fix it up? I mean, I'm getting a pretty nice wave now, but
there is still some distortion that you can just see at the top of the peaks
on the yellow trace.

How do you control the peak voltages of an LC resonattor without mangling
the waveform? The waveform at the junction of L1/C3 is of course quite
beautiful, how do I get it from there to the output? ;-)

I realize that I will need a buffer stage(s) before I can make any real use
of the signal, but I want the input to the buffer to be as perfect as
possible.

Thanks :-)




K7ITM March 19th 07 05:27 PM

LC Oscillator Questions
 
On Mar 19, 9:23 am, "Anthony Fremont" wrote:
Pictures available in ABSE

The top trace (yellow) is taken between C4 and R2. The bottom trace (cyan)
is taken at the base of the transistor. There is a switchercad file, but
the simulation will show allot of distortion that really isn't present in
the prototype circuit, because of lots of circuit capactance I suspect. R1
was something I was playing with to try and tame the voltage across L1/C3
being applied to the base.

Hello all,

I was tinkering with this LC oscillator (Colpitts/Clapp) this weekend. I
arrived at the values of C1 and C2 empirically after starting with a crystal
oscillator circuit. The values in the original circuit created a horrid
waveform that looked allot like the simulation. After much tinkering around
and simulating, I come to the conclusion that getting a perfect waveform is
nearly impossible, especially with big swing. It seems that the transistor
likes to take a bite out of the right half of the peak of the wave.

What is the secret to beautiful waveforms? Do I need another LC resonator
on the output to fix it up? I mean, I'm getting a pretty nice wave now, but
there is still some distortion that you can just see at the top of the peaks
on the yellow trace.

How do you control the peak voltages of an LC resonattor without mangling
the waveform? The waveform at the junction of L1/C3 is of course quite
beautiful, how do I get it from there to the output? ;-)

I realize that I will need a buffer stage(s) before I can make any real use
of the signal, but I want the input to the buffer to be as perfect as
possible.

Thanks :-)



The waveform in a high Q tank that's lightly coupled to the amplifier
should be very nearly sinusoidal. If in addition, the amplifier
remains linear and represents a constant impedance over the whole
cycle of the waveform, then the waveforms should everywhere be
sinusoidal. If the amplifier+tank has barely enough loop gain to
sustain oscillation, then clipping will be minimal, but it's also
possible to detect the level and control the gain of the amplifier.
You could, for example, use a light bulb like HP did in their original
audio oscillator. Beware, though, that best oscillator performance in
other regards may not be achieved the same way you achieve lowest
harmonic distortion. Be careful that you optimize the right things
for your application.

In the work I do, I need to measure distortion, and the generators I
use don't have low enough distortion in their outputs to be directly
useful. The distortion levels in the "raw" outputs are generally
about -40 to -50dBc. I use filters to make things better, and can get
to -140dBc distortion levels fairly easily. If it's low harmonic
distortion you want, I'd suggest that it may be better to just put a
filter on the output of the oscillator that has only moderately low
harmonic output, and not worry so much about that aspect of oscillator
performance. Filters work well when the oscillator frequency range is
about 1.5:1 or less. Much more than that and you'd need to switch in
different filters depending on the oscillator frequency.

Cheers,
Tom


Helmut Sennewald March 19th 07 05:31 PM

LC Oscillator Questions
 
Hello Anthony,

1.
Please set the following option to sitch off data reduction/compression
in the result file..

..options plotwinsize=0

2.
You have to set a small maximum timestep in the .TRAN line too.
Maybe a value of 0.01*Period of oscillation if you hunt for very low
distortion.


Can you send me your file (.asc-file and model-file?) to check it?

Best regards,
Helmut




"Anthony Fremont" schrieb im Newsbeitrag
...
Pictures available in ABSE

The top trace (yellow) is taken between C4 and R2. The bottom trace
(cyan)
is taken at the base of the transistor. There is a switchercad file, but
the simulation will show allot of distortion that really isn't present in
the prototype circuit, because of lots of circuit capactance I suspect.
R1
was something I was playing with to try and tame the voltage across L1/C3
being applied to the base.


Hello all,

I was tinkering with this LC oscillator (Colpitts/Clapp) this weekend. I
arrived at the values of C1 and C2 empirically after starting with a
crystal
oscillator circuit. The values in the original circuit created a horrid
waveform that looked allot like the simulation. After much tinkering
around
and simulating, I come to the conclusion that getting a perfect waveform
is
nearly impossible, especially with big swing. It seems that the
transistor
likes to take a bite out of the right half of the peak of the wave.

What is the secret to beautiful waveforms? Do I need another LC resonator
on the output to fix it up? I mean, I'm getting a pretty nice wave now,
but
there is still some distortion that you can just see at the top of the
peaks
on the yellow trace.

How do you control the peak voltages of an LC resonattor without mangling
the waveform? The waveform at the junction of L1/C3 is of course quite
beautiful, how do I get it from there to the output? ;-)

I realize that I will need a buffer stage(s) before I can make any real
use
of the signal, but I want the input to the buffer to be as perfect as
possible.

Thanks :-)






Tim Wescott March 19th 07 05:40 PM

LC Oscillator Questions
 
Anthony Fremont wrote:
Pictures available in ABSE

The top trace (yellow) is taken between C4 and R2. The bottom trace (cyan)
is taken at the base of the transistor. There is a switchercad file, but
the simulation will show allot of distortion that really isn't present in
the prototype circuit, because of lots of circuit capactance I suspect. R1
was something I was playing with to try and tame the voltage across L1/C3
being applied to the base.


Hello all,

I was tinkering with this LC oscillator (Colpitts/Clapp) this weekend. I
arrived at the values of C1 and C2 empirically after starting with a crystal
oscillator circuit. The values in the original circuit created a horrid
waveform that looked allot like the simulation. After much tinkering around
and simulating, I come to the conclusion that getting a perfect waveform is
nearly impossible, especially with big swing. It seems that the transistor
likes to take a bite out of the right half of the peak of the wave.

What is the secret to beautiful waveforms? Do I need another LC resonator
on the output to fix it up? I mean, I'm getting a pretty nice wave now, but
there is still some distortion that you can just see at the top of the peaks
on the yellow trace.

How do you control the peak voltages of an LC resonattor without mangling
the waveform? The waveform at the junction of L1/C3 is of course quite
beautiful, how do I get it from there to the output? ;-)

I realize that I will need a buffer stage(s) before I can make any real use
of the signal, but I want the input to the buffer to be as perfect as
possible.

Thanks :-)



The secret to a beautiful waveform is -- you usually don't need it
straight from the oscillator.

There are a lot of things that you want out of an LC oscillator. Low
phase noise, frequency stability, consistently strong oscillation, pure
tone, etc. Of these, the only two that you can't clean up later in the
following amplifier chain is low phase noise and frequency stability.
Concentrate on those, & don't sweat the nice waveform.

Frequency stability and phase noise performance are often achieved by
intentionally designing the amplifier so the active element operates in
class C, without ever going into voltage saturation. This keeps it's
drain (or collector) impedance high, yet delivers a large voltage swing
to the gate (or base) to keep phase noise low. It also gives you a more
or less consistent standing voltage in the tank, which helps the design
of the following buffer stages.

If you absolutely positively must tap the World's Most Beautiful Sine
Wave off of the oscillator section, consider a parallel-tuned tank
that's loosely coupled to the active element. Then loosely couple your
output tap to that -- it's your best chance.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

Anthony Fremont March 19th 07 06:34 PM

LC Oscillator Questions
 
K7ITM wrote:
On Mar 19, 9:23 am, "Anthony Fremont" wrote:
The waveform in a high Q tank that's lightly coupled to the amplifier
should be very nearly sinusoidal. If in addition, the amplifier
remains linear and represents a constant impedance over the whole
cycle of the waveform, then the waveforms should everywhere be
sinusoidal. If the amplifier+tank has barely enough loop gain to
sustain oscillation, then clipping will be minimal, but it's also
possible to detect the level and control the gain of the amplifier.
You could, for example, use a light bulb like HP did in their original
audio oscillator. Beware, though, that best oscillator performance in
other regards may not be achieved the same way you achieve lowest
harmonic distortion. Be careful that you optimize the right things
for your application.


After reading the other replies, it seems aparent that the shape of the
signal from the first stage is not that critical, it is stability and phase
noise that are most important. So, I should put things back where there is
clipping to be sure that the oscillator oscillates and then clean up the
signal in subsequent stages.

In the work I do, I need to measure distortion, and the generators I
use don't have low enough distortion in their outputs to be directly
useful. The distortion levels in the "raw" outputs are generally
about -40 to -50dBc. I use filters to make things better, and can get
to -140dBc distortion levels fairly easily. If it's low harmonic
distortion you want, I'd suggest that it may be better to just put a
filter on the output of the oscillator that has only moderately low
harmonic output, and not worry so much about that aspect of oscillator
performance. Filters work well when the oscillator frequency range is
about 1.5:1 or less. Much more than that and you'd need to switch in
different filters depending on the oscillator frequency.


Thanks. :-)



Anthony Fremont March 19th 07 06:39 PM

LC Oscillator Questions
 
Helmut Sennewald wrote:
Hello Anthony,

1.
Please set the following option to sitch off data
reduction/compression in the result file..

.options plotwinsize=0

2.
You have to set a small maximum timestep in the .TRAN line too.
Maybe a value of 0.01*Period of oscillation if you hunt for very low
distortion.


Can you send me your file (.asc-file and model-file?) to check it?


In alt.binaries.schematics.electronic I have posted the schematic, the
asc-file and an oscilloscope screen shot from an actual circuit. Here is
the asc-file contents:

Version 4
SHEET 1 880 708
WIRE -704 -96 -784 -96
WIRE -400 -96 -704 -96
WIRE -224 -96 -400 -96
WIRE -704 -16 -704 -96
WIRE -400 -16 -400 -96
WIRE -224 32 -224 -96
WIRE -544 80 -592 80
WIRE -400 80 -400 64
WIRE -400 80 -464 80
WIRE -288 80 -400 80
WIRE -592 128 -592 80
WIRE -400 144 -400 80
WIRE -784 160 -784 -96
WIRE -400 240 -400 208
WIRE -224 240 -224 128
WIRE -224 240 -400 240
WIRE -80 240 -224 240
WIRE 48 240 -16 240
WIRE -784 272 -784 240
WIRE -704 272 -704 48
WIRE -592 272 -592 208
WIRE -400 272 -400 240
WIRE -224 288 -224 240
WIRE -592 384 -592 336
WIRE -400 384 -400 336
WIRE -400 384 -592 384
WIRE -224 384 -224 368
WIRE -224 384 -400 384
WIRE -400 448 -400 384
FLAG -784 272 0
FLAG -400 448 0
FLAG -704 272 0
FLAG 48 320 0
SYMBOL voltage -784 144 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V1
SYMATTR Value 5.8
SYMBOL res -416 -32 R0
SYMATTR InstName R3
SYMATTR Value 100k
SYMBOL npn -288 32 R0
SYMATTR InstName Q3
SYMATTR Value 2N3904
SYMBOL cap -416 144 R0
SYMATTR InstName C1
SYMATTR Value .01µ
SYMBOL res -240 272 R0
SYMATTR InstName R7
SYMATTR Value 1k
SYMBOL cap -416 272 R0
SYMATTR InstName C2
SYMATTR Value 500p
SYMBOL ind -608 112 R0
SYMATTR InstName L1
SYMATTR Value 20µ
SYMATTR SpiceLine Rser=.1
SYMBOL cap -608 272 R0
SYMATTR InstName C3
SYMATTR Value 200p
SYMBOL cap -16 224 R90
WINDOW 0 0 32 VBottom 0
WINDOW 3 32 32 VTop 0
SYMATTR InstName C4
SYMATTR Value 270p
SYMBOL res -448 64 R90
WINDOW 0 0 56 VBottom 0
WINDOW 3 32 56 VTop 0
SYMATTR InstName R1
SYMATTR Value .001
SYMBOL cap -720 -16 R0
SYMATTR InstName C5
SYMATTR Value 10µ
SYMBOL res 32 224 R0
SYMATTR InstName R2
SYMATTR Value 10000k
TEXT -792 360 Left 0 !.tran 50uS

Thank you for your time.


Best regards,
Helmut




"Anthony Fremont" schrieb im Newsbeitrag
...
Pictures available in ABSE

The top trace (yellow) is taken between C4 and R2. The bottom trace
(cyan)
is taken at the base of the transistor. There is a switchercad
file, but the simulation will show allot of distortion that really
isn't present in the prototype circuit, because of lots of circuit
capactance I suspect. R1
was something I was playing with to try and tame the voltage across
L1/C3 being applied to the base.


Hello all,

I was tinkering with this LC oscillator (Colpitts/Clapp) this
weekend. I arrived at the values of C1 and C2 empirically after
starting with a crystal
oscillator circuit. The values in the original circuit created a
horrid waveform that looked allot like the simulation. After much
tinkering around
and simulating, I come to the conclusion that getting a perfect
waveform is
nearly impossible, especially with big swing. It seems that the
transistor
likes to take a bite out of the right half of the peak of the wave.

What is the secret to beautiful waveforms? Do I need another LC
resonator on the output to fix it up? I mean, I'm getting a pretty
nice wave now, but
there is still some distortion that you can just see at the top of
the peaks
on the yellow trace.

How do you control the peak voltages of an LC resonattor without
mangling the waveform? The waveform at the junction of L1/C3 is of
course quite beautiful, how do I get it from there to the output? ;-) I
realize that I will need a buffer stage(s) before I can make any
real use
of the signal, but I want the input to the buffer to be as perfect as
possible.

Thanks :-)




Helmut Sennewald March 19th 07 07:21 PM

LC Oscillator Questions
 
"Anthony Fremont" schrieb im Newsbeitrag
...
Helmut Sennewald wrote:
Hello Anthony,

1.
Please set the following option to sitch off data
reduction/compression in the result file..

.options plotwinsize=0

2.
You have to set a small maximum timestep in the .TRAN line too.
Maybe a value of 0.01*Period of oscillation if you hunt for very low
distortion.


Can you send me your file (.asc-file and model-file?) to check it?


In alt.binaries.schematics.electronic I have posted the schematic, the
asc-file and an oscilloscope screen shot from an actual circuit. Here is
the asc-file contents:



Hello Anthony,

The large capacitance of C1 (10nF) has caused an interrupted oscillation.
Please change its value to 1000p and the oscillator will work as expected.
I have also added MEASURE-commands to measure the frequency.
View - SPICE Error Log

Another method is using the FFT in the waveform viewer.

Best regards,
Helmut

Save as "osc1.asc".

Version 4
SHEET 1 880 708
WIRE -688 -96 -784 -96
WIRE -576 -96 -688 -96
WIRE -304 -96 -576 -96
WIRE -784 -64 -784 -96
WIRE -688 -64 -688 -96
WIRE -576 -16 -576 -96
WIRE -304 32 -304 -96
WIRE -784 48 -784 16
WIRE -688 48 -688 0
WIRE -576 80 -576 64
WIRE -480 80 -576 80
WIRE -432 80 -480 80
WIRE -368 80 -432 80
WIRE -576 128 -576 80
WIRE -432 144 -432 80
WIRE -576 240 -576 208
WIRE -432 240 -432 208
WIRE -304 240 -304 128
WIRE -304 240 -432 240
WIRE -240 240 -304 240
WIRE -160 240 -240 240
WIRE -64 240 -96 240
WIRE -32 240 -64 240
WIRE -576 272 -576 240
WIRE -432 272 -432 240
WIRE -32 272 -32 240
WIRE -304 288 -304 240
WIRE -32 368 -32 352
WIRE -576 384 -576 336
WIRE -432 384 -432 336
WIRE -432 384 -576 384
WIRE -304 384 -304 368
WIRE -304 384 -432 384
WIRE -432 416 -432 384
FLAG -784 48 0
FLAG -432 416 0
FLAG -688 48 0
FLAG -32 368 0
FLAG -64 240 out
FLAG -240 240 e
FLAG -480 80 b
FLAG -576 240 lc
SYMBOL voltage -784 -80 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V1
SYMATTR Value 5.8
SYMBOL res -592 -32 R0
SYMATTR InstName R3
SYMATTR Value 100k
SYMBOL npn -368 32 R0
SYMATTR InstName Q3
SYMATTR Value 2N3904
SYMBOL cap -448 144 R0
SYMATTR InstName C1
SYMATTR Value 1000p
SYMBOL res -320 272 R0
SYMATTR InstName R7
SYMATTR Value 1k
SYMBOL cap -448 272 R0
SYMATTR InstName C2
SYMATTR Value 500p
SYMBOL ind -592 112 R0
WINDOW 39 36 108 Left 0
SYMATTR InstName L1
SYMATTR Value 20µ
SYMATTR SpiceLine Rser=.1
SYMBOL cap -592 272 R0
SYMATTR InstName C3
SYMATTR Value 200p
SYMBOL cap -96 224 R90
WINDOW 0 0 32 VBottom 0
WINDOW 3 32 32 VTop 0
SYMATTR InstName C4
SYMATTR Value 270p
SYMBOL cap -704 -64 R0
SYMATTR InstName C5
SYMATTR Value 10µ
SYMBOL res -48 256 R0
SYMATTR InstName R2
SYMATTR Value 100k
TEXT -824 -152 Left 0 !.tran 0 200uS 0 4n
TEXT -824 -184 Left 0 !.options plotwinsize=0
TEXT -816 472 Left 0 !.measure tran t1 FIND time WHEN V(out)=0 TD=90u RISE=1
TEXT -816 504 Left 0 !.measure tran t2 FIND time WHEN V(out)=0 TD=90u
RISE=101
TEXT -816 536 Left 0 !.measure tran f0 PARAM 100/(t2-t1)
TEXT -816 576 Left 0 ;View - SPICE Error Log \nfor the measured frequency
TEXT -520 -184 Left 0 ;C1 changed to 1000p!



Anthony Fremont March 19th 07 08:07 PM

LC Oscillator Questions
 
Tim Wescott wrote:

The secret to a beautiful waveform is -- you usually don't need it
straight from the oscillator.


Okay..

There are a lot of things that you want out of an LC oscillator. Low
phase noise, frequency stability, consistently strong oscillation,
pure tone, etc. Of these, the only two that you can't clean up later
in the following amplifier chain is low phase noise and frequency
stability. Concentrate on those, & don't sweat the nice waveform.


Okay, that certainly explains why all the sample circuits I find don't
expend any great effort at creaing a nice sine wave, and none at explaining
why. What you say certainly makes sense, especially if there are no really
negative consequences of having the oscillator make a "less than perfectly
shaped" wave.

Frequency stability and phase noise performance are often achieved by
intentionally designing the amplifier so the active element operates
in class C, without ever going into voltage saturation. This keeps
it's drain (or collector) impedance high, yet delivers a large
voltage swing to the gate (or base) to keep phase noise low. It also
gives you a more or less consistent standing voltage in the tank,
which helps the design of the following buffer stages.

If you absolutely positively must tap the World's Most Beautiful Sine
Wave off of the oscillator section, consider a parallel-tuned tank
that's loosely coupled to the active element. Then loosely couple
your output tap to that -- it's your best chance.


Ok, thanks for the information. :-) I did allot of googling but found
nothing that explained it like this. I was thinking of building a little
single conversion superhet WWV receiver for 10MHz, if I continue with that
I'll just concentrate on cleaning it up in another stage.

Some material I read suggested keeping Xl of L1 at ~300Ohms, the series Xc
(C3) at ~200Ohms and Xc of C1/C2 at 45Ohms. Do you have any thoughts on
that? Right now I have way too much inductance for 3.5MHz by that theory,
and judging from other circuits I've seen. 10uH seems to be the going thing
for around 4MHz?



Tam/WB2TT March 19th 07 08:46 PM

LC Oscillator Questions
 

"Anthony Fremont" wrote in message
...
K7ITM wrote:
On Mar 19, 9:23 am, "Anthony Fremont" wrote:
The waveform in a high Q tank that's lightly coupled to the amplifier
should be very nearly sinusoidal. If in addition, the amplifier
remains linear and represents a constant impedance over the whole
cycle of the waveform, then the waveforms should everywhere be
sinusoidal. If the amplifier+tank has barely enough loop gain to
sustain oscillation, then clipping will be minimal, but it's also
possible to detect the level and control the gain of the amplifier.
You could, for example, use a light bulb like HP did in their original
audio oscillator. Beware, though, that best oscillator performance in
other regards may not be achieved the same way you achieve lowest
harmonic distortion. Be careful that you optimize the right things
for your application.


After reading the other replies, it seems aparent that the shape of the
signal from the first stage is not that critical, it is stability and
phase noise that are most important. So, I should put things back where
there is clipping to be sure that the oscillator oscillates and then clean
up the signal in subsequent stages.

I have never seen clipping. These things are supposed to limit in cutoff,
not saturation. As the signal build up, the conduction angle gets smaller
and smaller until the device runs out of gain. That is another way of saying
that the DC value of the gate voltage gets more negative the bigger the
amplitude. This works out automatically with a JFET. You need about 10K -
100K DC resistance from gate to ground. Using a bipolar transistor is not a
good idea.

Tam



Tim Wescott March 19th 07 08:48 PM

LC Oscillator Questions
 
Anthony Fremont wrote:

Tim Wescott wrote:


The secret to a beautiful waveform is -- you usually don't need it
straight from the oscillator.



Okay..


There are a lot of things that you want out of an LC oscillator. Low
phase noise, frequency stability, consistently strong oscillation,
pure tone, etc. Of these, the only two that you can't clean up later
in the following amplifier chain is low phase noise and frequency
stability. Concentrate on those, & don't sweat the nice waveform.



Okay, that certainly explains why all the sample circuits I find don't
expend any great effort at creaing a nice sine wave, and none at explaining
why. What you say certainly makes sense, especially if there are no really
negative consequences of having the oscillator make a "less than perfectly
shaped" wave.


Frequency stability and phase noise performance are often achieved by
intentionally designing the amplifier so the active element operates
in class C, without ever going into voltage saturation. This keeps
it's drain (or collector) impedance high, yet delivers a large
voltage swing to the gate (or base) to keep phase noise low. It also
gives you a more or less consistent standing voltage in the tank,
which helps the design of the following buffer stages.

If you absolutely positively must tap the World's Most Beautiful Sine
Wave off of the oscillator section, consider a parallel-tuned tank
that's loosely coupled to the active element. Then loosely couple
your output tap to that -- it's your best chance.



Ok, thanks for the information. :-) I did allot of googling but found
nothing that explained it like this. I was thinking of building a little
single conversion superhet WWV receiver for 10MHz, if I continue with that
I'll just concentrate on cleaning it up in another stage.

Some material I read suggested keeping Xl of L1 at ~300Ohms, the series Xc
(C3) at ~200Ohms and Xc of C1/C2 at 45Ohms. Do you have any thoughts on
that? Right now I have way too much inductance for 3.5MHz by that theory,
and judging from other circuits I've seen. 10uH seems to be the going thing
for around 4MHz?


That sounds more or less right. With a Clapp oscillator the main tank
is isolated by the series cap, so more of the energy is kept in the coil
and C3, and less of it shows up in C1, C2, and the transistor.

If you're driving a balanced mixer you want to have an LO signal that
doesn't have much even-harmonic (2nd, 4th, etc.) energy in it, but for a
casual receiver that's the least of your worries. Since you're
operating at a fixed frequency it may be a good idea to just feed the
oscillator output into a single-tuned resonant circuit to clean it up,
then send it on to the mixer.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html


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