VSWR of a Cascaded System
v...@my-dejanews.com
way to find out the input and the output VSWR given the VSWR of the
individual components?
Many thanks.
VB
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v...@my-dejanews.com
other words, if the VSWR for each component is known, can the input and
output VSWR of the entire system be found?
Mark Kinsler
>Is there a method to determine the VSWR of a cascaded set of components? In
>other words, if the VSWR for each component is known, can the input and
>output VSWR of the entire system be found?
I think the VSWR can be either defined as, or somehow converted to the
ratio of transmitted power to reflected power. If you know that for each
component, could you figure the ratio for the entire string? Hmmm. I'll
think about that one. But I'm pretty sure that there's a method for
cascading the figures--I've forgotten.
Mark Kinsler
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Interpretation and instruction of physical science and technology
Athens, Ohio, USA. http://www.frognet.net/~kinsler
Roy McCammon
>
> Is there a method to determine the VSWR of a cascaded set of components? In
> other words, if the VSWR for each component is known, can the input and
> output VSWR of the entire system be found?
I'm dredging up old memories here, but I think,
yes there is a method, but you need a full set
of two port parameters (four parameters in
all, possibly complex) for each component.
There are many different sets of two port
parameters, each of which can be transformed
into any of the others. One such set would be
impedance's looking into each side of the two port
and propagation constant (loss and phase shift)
each direction. You might look up scattering
matrixes and two-ports for more info.
Opinions expressed herein are my own and may not represent those of my employer.
Peter Somlo
You are right Roy. From any parameter set you can convert to the 'T'
(transmission ) parameters, which when multiplied (as matrixes) will
yield the T parameters of the cascaded set. Then you can convert back.
[See for instance: Somlo & Hunter, 'Microwave Impedance Measurement',
Peregrinus 1985, p. 20.]
Peter
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Philip G.Coady
measure of the
degree of impedance match (or mismatch between 2 systems).
System "A" has an output impedance and system "B" has an input impedance, the
degree of
mismatch between the 2 impedance's gives rise to return loss or VSW's. When a
mismatch is
present ,part or all of the incident signal is reflected back towards the source
giving rise to a
standing wave caused by the addition of the incident and reflected waves
I am dredging up old memories here. But if you convert VSWR to Return loss there
is a
formula to calculate return loss if you know the input and output impedance's of
both
networks. I THINK the formula is as follows....
Return loss = -10log[(Zout - Zin)/(Zout + Zin)] in dB
ie if Zout = Zin then the return loss is infinite(or is it zero)???, a perfectly
matched system
VSWR = 1/Return loss
Knowing the VSWR of each component you could calculate Zout and Zin on a per
unit basis.
You then just do all the number crunching to get the new Zout (looking back
upstream from
the last component) and the new Zin (looking down stream from the first
component).
You will have to get your network theory book out for this.
Plug these new Zin and Zout for the whole system to get the VSWR ( or return
loss) of the
system.
I may have some of the math wrong but the concept is sound.
Hope this helps
Phil
v...@my-dejanews.com wrote:
> Is there a method to determine the VSWR of a cascaded set of components? In
> other words, if the VSWR for each component is known, can the input and
> output VSWR of the entire system be found?
>
Josh Nickel
> First things first, there is no such thing as input or output VSWR. VSWR is a
> measure of the
> degree of impedance match (or mismatch between 2 systems).
>
> System "A" has an output impedance and system "B" has an input impedance, the
> degree of
> mismatch between the 2 impedance's gives rise to return loss or VSW's. When a
> mismatch is
> present ,part or all of the incident signal is reflected back towards the source
> giving rise to a
> standing wave caused by the addition of the incident and reflected waves
>
>
> I am dredging up old memories here. But if you convert VSWR to Return loss there
> is a
> formula to calculate return loss if you know the input and output impedance's of
> both
> networks. I THINK the formula is as follows....
>
> Return loss = -10log[(Zout - Zin)/(Zout + Zin)] in dB
>
> ie if Zout = Zin then the return loss is infinite(or is it zero)???, a perfectly
> matched system
>
>
> VSWR = 1/Return loss
>
Actually the formula is
Return Loss = -10 log [|Gamma|^2]
where Gamma is the complex reflection coefficient and |Gamma| is the
magnitude of this complex number. The return loss is defined as the 'lost'
power in the sense of that amount of power which isn't absorbed in a load.
For example, a perfectly matched load has Gamma = 0; thus RL = Inf dB. In
other words, none of the power is lost (-Inf dB) to reflections back
toward the source. Gamma is defined as
Gamma = (Zin - Zchar)/(Zin+Zchar);
wher Zchar is the characteristic impedance of the reference system
(usually a 50 ohm cable)
The SWR (or standing wave ratio) defines the ratio between the standing
wave maximum magnitude (Vmax) and minimum magnitude (Vmin).
Vmax = 1 + |Gamma|
Vmin = 1 - |Gamma|
And therefore
SWR = Vmax/Vmin = (1 + |Gamma|)/(1 - |Gamma|)
or
|Gamma| = (SWR-1)/(SWR+1)
In regards to the original question about SWR of a cascaded system, you
would have to calculate the input reflection coefficient of the system.
Cascading the S-parameters of all the devices would be the recommended way
to do it. This technique is described in most microwave textbooks
(Pozar's "Microwave Engineering" gives a great example). I assume in your
system you have some series of devices and you want to find the input SWR,
with the output terminated in some known load impedance. Once you
determine the input Gamma (looking into the system), find the SWR with the
formula above.
Here's an example (poor, but illustrates the point): suppose you have a
receiver, a preamp, a matching network and an antenna. You want to find
the SWR (or the mismatch) that the receiver 'sees' looking toward the
antenna. Assume you know the antenna impedance, and you know the
S-parameters of the matching network (Smatch) and the preamp (Samp). To
find the input impedance seen by the receiver, first consider the antenna
and matching network. The impedance looking into the matching network
towards the antenna is
Gamma_in_match = [Smatch]_11 + ([Smatch]_21 * [Smatch]_12 * Gamma_antenna)
/(1 - [Smatch]_22 * Gamma_antenna)
Now, Gamma_in_match becomes the load impedance of the preamp. Thus
Gamma_in_amp = [Samp]_11 + ([Samp]_21 * [Samp]_12 * Gamma_in_match)
/(1 - [Samp]_22 * Gamma_in_match)
And Gamma_in_amp is thus the input reflection coefficient of the system.
Use the formula above and you have the input SWR. Note: the above example
is only valid if all your devices are 2-ports. Otherwise, the math becomes
considerably more complicated.
HTH,
Josh
Morra
If you assume that each element has the same return loss and they are
independent variables, then the return loss drops by 3 dB every time
you double the number of components.
For example, suppose each component has a return loss of 40 dB.
Two elements have a return loss of 37 dB.
Four elements have a return loss of 34 dB.
Eight elements have a return loss of 31 dB.
In article <6u657p$ell$1...@nnrp1.dejanews.com>, v...@my-dejanews.com wrote:
>I'm trying to determine the overall VSWR of a cascaded system. Is there any
>way to find out the input and the output VSWR given the VSWR of the
>individual components?
>
cah...@ibm.net
>I'm trying to determine the overall VSWR of a cascaded system. Is there any
>way to find out the input and the output VSWR given the VSWR of the
>individual components?
>
>Many thanks.
>
>VB
>
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For a passive ( no amplifiers), losseless system the worst case VSWR can be
found by multipling the individual VSWRs. The worst case occurs when all of
the mismatches add in phase.
Don Runyon
v...@my-dejanews.com wrote in message <6u657p$ell$1...@nnrp1.dejanews.com>...
>I'm trying to determine the overall VSWR of a cascaded system. Is there any
>way to find out the input and the output VSWR given the VSWR of the
>individual components?
>
>Many thanks.
>
>VB
>
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You have received many responses, and few answers. I will help you.
First, convert VSWR to a Voltage reflection coefficient, Gamma,
Gamma=(VSWR-1)/(VSWR+1)
Now, you only have information about the modulus of the component reflection
coefficient. The phase is unknown. Also, you have no information about the
transmission characteristics (Magnitute & Phase) of the component in either
direction which is necessary for a more complete analysis. Hence, an
analysis of a cascaded system must be carried out with some simplifying
assumptions. Assuming the components are "low loss" devices, and the
input/output VSWR (return losses) are the same, and the individual component
reflection coefficients are small, then the equation for a worst case
analysis is simply:
Gamma Total = gamma1 + gamma2 + gamma3 + ....
In such an case, each time you add 2 equal valued reflection coefficients
the sum voltage reflection coefficient increases by 6 dB
Gamma(dB)=20*log(gamma)).
Worst case analysis is usually too pessimistic in practice. A more
realistic estimate is obtained for several cascaded components by taking the
Root-Sum-Square (RSS) of the individual reflection coefficients:
Gamma Total = SQRT( gamma1*gamma1 + gamma2*gamma2 + ...)
These two methods bound the problem from a typical response to a worst case
one. If the prior assumptions are invalid, you need more information on
each component. A full Scattering (S-) Parameter description of each
component can be defined or measured and exact formulas applied to give the
overall cascade system response. You can always simplify the analysis
starting with a complete S-parameter approach and reducing the problem from
there based on known information.
cah...@ibm.net
Summing the reflection coefficients does not give the worst case. Consider
the case with 11 of reflections with a reflection coeff. magnitudue of 0.1.
The total reflection coefficient would be 1.1 which makes no sense. Adding the
reflection coefficients ignores the effect of multiple relections. The correct
worst case value is found by multipling the VSWRs. For the above example this
yields a worst case reflection coefficient of 0.8.
Don Runyon
"If the prior assumptions are invalid, you need more information on
>>each component. A full Scattering (S-) Parameter description of each
>>component can be defined or measured and exact formulas applied to give
the
>>overall cascade system response. You can always simplify the analysis
>>starting with a complete S-parameter approach and reducing the problem
from
>>there based on known information."
In the (complete) S-parameter solution there is a term in the denominator
of each "component" reflection (and interaction term) to properly normalize
and avoid the problem with the solution you have described. Of course if
you add a large number (or infinite) number of small reflections using the
approximate solution I gave, you will easily violate conservation of power.
If you add more than a few (say 2 or 3) -20 dB magnitude as you have, you
will violate the initial assumptions. If you want the exact answer, use
cascaded s-parameters. If your working with a handful of reasonably matched
components (say -25 to -30 dB return loss) and want to do some evaluation on
your hand calculator, then you can use the simple approach. It is
reasonably accurate for small reflections.
By the way, multiplying the VSWR's is not an exact solution, just another
(and different) approximation.
cah...@ibm.net wrote in message <3623d...@news1.ibm.net>...