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Post subject: Cascade of amplifiers at 1 GHz Posted: Mon Mar 10, 2008 2:28 am


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.



Post subject: Posted: Mon Mar 10, 2008 11:54 am


Joined: Thu Sep 25, 2003 1:19 am

Posts: 50

Location: texarcana

Have you tried reactive matching? What is your bandwidth?




Post subject: Posted: Mon Mar 10, 2008 2:21 pm


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.



Post subject: Posted: Mon Mar 10, 2008 2:41 pm


Joined: Wed Feb 22, 2006 3:51 pm

Posts: 104


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.




Post subject: Posted: Mon Mar 10, 2008 3:27 pm


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?



Post subject: cascaded amplifiersPosted: Mon Mar 10, 2008 5:24 pm


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!




Post subject: Posted: Mon Mar 10, 2008 6:08 pm


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!



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:




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.

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