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Cascade of amplifiers at 1 GHz - RF Cafe Forums
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sfnative
Post subject: Cascade of amplifiers at 1 GHz Posted: Mon
Mar 10, 2008 2:28 am
Lieutenant
Joined: Sun Mar 09, 2008
11:03 pm
Posts: 4
Location: San Francisco
When cascading amplifiers
(i.e. ADL5542), should I worry about a reflection from the input of
stage 2 passing back through stage 1 then being amplified forward along
with the original? The specs are 20 dB gain(S21), -15 dB input return
loss (S11), and -22 dB isolation (S12).
It seems to me that
I'll have a delayed copy of the original at -17 dBc, plus anything reflected
from the mixer that follows. Adding a 10dB pad would knock that to -37
dBc, but then my total gain cuts in half and I need twice as many stages.
I'm trying to get a -50 dBm signal up to (at least) -10 dBm
for the mixer (ADL5387) I'm looking to maintain 70 dB dynamic range
throughout.
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yendori
Post subject: Posted:
Mon Mar 10, 2008 11:54 am
General
Joined: Thu Sep
25, 2003 1:19 am
Posts: 50
Location: texarcana
Have you tried
reactive matching? What is your bandwidth?
Yendori
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sfnative
Post subject: Posted: Mon Mar 10, 2008
2:21 pm
Lieutenant
Joined: Sun Mar 09, 2008 11:03 pm
Posts: 4
Location: San Francisco
The BW is 500 MHz, 950 to 1450.
I don't know well enough how to improve the directivity with reactive
matching. What has me confused is that I don't see how anyone could
ever use one of these parts since so little gain is had when sufficient
pad is used to knock down the reflected signal.
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fred47
Post subject: Posted: Mon Mar 10, 2008 2:41 pm
General
Joined: Wed Feb 22, 2006 3:51 pm
Posts: 104
Hi!
I think that you may be trying to separate out the various
effects (gain, feedback) as isolated meanings for the S parameters.
That's not surprising, as trainers tend to identify S21 as gain, and
S12 as feedback, without all the qualifiers and explanations to those
terms. This is especially a problem for people with low-frequency experience
as they attempt to move up in frequency.
But there is no way
to measure S12 independently from S21. They are already linked by the
very act of taking the measurement of a single part, which doesn't distinguish
S12 from S21.
So, while you absolutely do need to be concerned
about reflections from the mixer - especially for undesired frequencies
such as image frequencies - you don't need to be as concerned as you
are about signal propagation backwards and forwards - those effects
are already implicitly there.
You probably want to convert from
S-parameters to either T-parameters or ABCD "chain" parameters to figure
out the effects of cascading two of these parts. You might be pleasantly
surprised.
fred
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sfnative
Post subject:
Posted: Mon Mar 10, 2008 3:27 pm
Lieutenant
Joined: Sun
Mar 09, 2008 11:03 pm
Posts: 4
Location: San Francisco
So
intuitively, a reverse propagating signal would be seen as a disturbance
- an error - that the amplifier would then compensate for. To compensate,
a small signal would be fed back from the output to the input port that,
through the forward gain, would cancel most of the original signal.
The error in that compensation would then be the output return loss,
S22.
The isolation, S12, would come from the small feedback
signal being that much smaller than the "input" at port 2.
Then
the thing to think of is that the reverse propagating signal will travel
to the preceeding stage where the output return loss will reflect a
now forward propagating signal that will be amplified, etc..
Am I thinking this through correctly?
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fred47
Post subject: cascaded amplifiersPosted: Mon Mar 10, 2008 5:24 pm
General
Joined: Wed Feb 22, 2006 3:51 pm
Posts:
104
The best thing to do is to focus on what the S parameters mean,
and how they're measured.
They're measured in a perfectly-terminated
system, usually 50 Ohms. Keep your eye on the direction of the power
flow:
S11 is measuring the power reflected from port 1 (the
"input" port, though that label is somewhat arbitrary), when it is driven
from a 50 Ohm generator (in other words, a known power flows into port
1). We don't care how it actually got there, just that it's flowing
back out from port 1.
S22 is measuring the power reflected from
port 2 (the "output" port), when it's driven from a 50 Ohm generator.
(Just exactly switching the port 1 and port 2 labels!)
S21 is
measuring the power flowing out of port 2 when port 1 is driven with
a known power.
S12 is measuring the power flowing out of port
1 when port 2 is driven with a known power.
If no power flows
INTO port 2, then the only power flowing out of port 1 is the reflected
power.
The only way power flows into port 2 is if it's driving
a mis-matched load (but mixers are guaranteed to be poor matches <grin>)
When you have two amplifiers cascaded, the power flowing into
port 2 of the first amplifier is the power reflected from port 1 of
the second amplifier, plus any power coming back into the output of
the second amplifier from the load, attenuated by S12 of the second
amplifier.
Changing topics a bit:
You can check my math,
but what I get for the s-parameters of the cascaded amplifier at 900
MHz is (dB/angle in degrees form)
-37.918 -178.634 40.149 -95.889
-44.988 -42.515 -20.439 -125.360
This was converting S-Parameters
to ABCD or "chain" parameters, multiplying, and converting back, all
based on 50 Ohms.
I hope this helps, and that I've not muddied
the waters too much!
Fred
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sfnative
Post subject: Posted: Mon Mar 10, 2008 6:08 pm
Lieutenant
Joined: Sun Mar 09, 2008 11:03 pm
Posts: 4
Location: San Francisco
OK. I'm going to cozy up with Hayward tonight. He's got a good chapter
on combining two-port networks. You've convinced me the math is worth
it.
They warned me RF was more than knowing to not multiply
decibels...
Thanks Fred!
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IR
Post
subject: Posted: Tue Mar 11, 2008 5:19 pm
Site Admin
Joined: Mon Jun 27, 2005 2:02 pm
Posts: 373
Location: Germany
Hello sfnative,
Putting Fred's excellent explanations about
S-parametrs into equations, will give the follows:
b1=S11*a1+S12*a2
b2=S22*a2+S21*a1
Where:
a1, a2 are the incident
waves at the input and output ports respectively.
b1, b2 are the
reflected waves at the input and output respectively.
From these
equations you can drive the following relations:
S11=b1/a1 @
a2=0 (Output port is terminated)
S12=b1/a2 @ a1=0 (Input port is
terminated).
S21=b2/a1 @ a2=0 (Output port is terminated)
S22=b2/a2
@ a1=0 (Input port is terminated)
From these relations you can
see that each S paramater is measured at a port (input or output) while
the other port is terminated and no power flows into or out of (Connected
to a load of characteristic impedance Zo).
S-parameters are
also used to define other paramaters such as Transducer Gain, stability
etc.
Posted
11/12/2012
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