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the responses to the original posts.
mhtplsh
Post subject: 50 Ohm TO 75 Ohm Posted: Wed Feb 21, 2007
12:53 pm
Captain
Joined: Wed Feb 21, 2007 12:50 pm
Posts: 18
Designing a 75 ohm input/output amplifier will require
S parameters with 75 ohm input output matching. Further the Smithchart
will also changed to 75 ohm impedance.
All the S parameters r available
in 50 ohms. How to convert them to 75 ohms.
Also input output impedance
calculated will be of 50 ohms as all the data is available in 50 ohms,
so this will also hv to be converted.
or
suggest anyother method
for designing 75 ohm amplifier with s parameter & smith chart.
Top
fred47
Post subject: 50 to 75 OhmPosted: Wed
Feb 21, 2007 1:44 pm
General
Joined: Wed Feb 22,
2006 3:51 pm
Posts: 104
Hi!
To get 75 Ohm s-parameters from
50 Ohm parameters, convert to impedance (for example, by plotting on
a Smith Chart normalized to 50 Ohms, or by formula), then convert to
75 Ohm s-parameters (for example, by plotting on a Smith Chart normalized
to 75 Ohms, or again by formula).
A reminder about the Smith
Chart: it's normalized to a value of unity for the center point ("prime
center", etc.). That means that every impedance you plot is divided
by the actual impedance. Philip Smith did that so that you'd always
be able to use the same chart. Straight impedances, like those you get
from a data sheet, aren't normalized, so if they give a value like "10+j5
Ohms" you can normalize and plot like always.
That means that
all the techniques that you've learned for 50 Ohms transfer directly
to 75 Ohms.
Formula: the impedance matrix can be calculated from
the scattering (s) matrix by this equation:
Z = (1+S)(1-S)^-1
and the scattering (s) matrix from the impedance matrix by
S=(Z-1)*(Z+1)^-1
A reminder that if S has eigenvalues of
+1 or -1, Z doesn't exist. (This isn't usually a problem, but just in
case...)
OK, an example (strictly made up, doesn't correspond
to any likely part!):
S11 = 0.5+1.0j S12 = 0.1 + 0j
S21 = 3.0
- 0.5j S22 = 1.0 + 0.1j
The normalized Z matrix is
-1.0 +
0.5j -0.5 + 0j
-15 + 2.5j -3.5 + 5.0j
and the 50-Ohm-denormalized
Z matrix is
-50 + 25j -25.+0j
-750 + 125j -175 + 250j
Now, normalize to 75 Ohms by dividing by 75. The 75-Ohm-normalized Z
matrix is
-0.66667 + 0.33333j -0.33333 + 0.00000j
-10.00000 +
1.66667j -2.33333 + 3.33333j
Finally, convert back to the scattering
(s) matrix:
0.16578 + 1.15508j 0.12834 + 0.03209j
4.01070 + 0.32086j
1.09626 + 0.16043j
I got the answers with the help of the GPL
program Octave - makes life a lot easier than using a calculator!
Good Luck!
Fred
Top
mhtplsh
Post subject:
Posted: Thu Feb 22, 2007 2:45 am
Captain
Joined: Wed
Feb 21, 2007 12:50 pm
Posts: 18
Got it! Thanks!
I will try
to get .xls file for coverting 50 ohm to 75 ohm as mentioned in another
post by jaya000. Here we hv discussed about NF.
I will calculate
on it & give u the results.
Top
mhtplsh
Post
subject: Posted: Thu Feb 22, 2007 4:53 am
Captain
Joined:
Wed Feb 21, 2007 12:50 pm
Posts: 18
This is what i got from .xls
file from Maxim
Ii this sheet i am not able to solve the solution
provided by Fred47.
Network Analyzer Impedance: 50
MAX3550/3553
Input Impedance: 75
S11, 50 ohm env. Impedance S11, 75 ohm env.
Freq. Real Image Real Image Real Image
1 0.53 -0.12 149.75 -51.00
0.37 -0.14
2 0.53 -0.12 148.77 -52.75 0.36 -0.15
3 0.53 -0.13
145.59 -55.14 0.36 -0.16
4 0.52 -0.14 142.66 -57.44 0.36 -0.17
5 0.52 -0.15 139.69 -59.71 0.35 -0.18
6 0.52 -0.16 136.83 -61.40
0.35 -0.19
7 0.51 -0.17 133.72 -63.43 0.34 -0.20
8 0.51 -0.18
130.63 -65.16 0.34 -0.21
9 0.51 -0.19 127.48 -66.63 0.33 -0.22
10 0.50 -0.19 124.44 -67.89 0.33 -0.23
For the same S parameters
of 50 ohms I am getting the following results.
For 100 Mhz. Calculated
on Vierpol in Elekta 50 ohms
Polar Rect
Input impedance Zi = 102.100
-65.3 42.664 -92.759
Output Impedence Zo = 233.22 -64 102.237
-209.617
For 100 Mhz. Calculated on Vierpol in Elekta 75 ohms
Polar Rect
Input impedance Zi = 86.630 -65.1 36.47 -78.577
Output Impedence Zo = 184.77 -58.7 96 -157.88
Top
mhtplsh
Post subject: Posted: Thu Feb 22, 2007 11:32 am
Captain
Joined: Wed Feb 21, 2007 12:50 pm
Posts: 18
Here is the weblink of the .pdf file. They hv also .xls file. The
50 ohm to 75 ohm in the previous reply hv been posted from this document.
http://www.eetchina.com/ARTICLES/2006MA ... _AN_08.PDF
Hope
this will be good for the people who want to know more.
Top
IR
Post subject: Posted: Thu Feb 22, 2007 11:42 am
Site Admin
Joined: Mon Jun 27, 2005 2:02 pm
Posts:
373
Location: Germany
Just to add to Fred's excellent post:
In any commercial RF design tool (ADS, Microwave Office, Eagleware
etc), you can define the Zo as you like and then plot the Smith Chart
based on the Zo you chose. This helps to avoid tedious calculations.
Top
mhtplsh
Post subject: Posted: Fri Feb 23, 2007
3:50 pm
Captain
Joined: Wed Feb 21, 2007 12:50 pm
Posts: 18
IR,
I understand that i should give input of 50ohm
s parameters & set the Zin/Zout as 75 ohms?
is this ok?
will the free RFSIM99 simulator will able to do this?
Top
IR
Post subject: Posted: Tue Feb 27, 2007 2:51 am
Site Admin
Joined: Mon Jun 27, 2005 2:02 pm
Posts:
373
Location: Germany
You should perform the S-parameters measurments
in a 50 ohm impedance environment i.e. the regular way.
The
impedances which you get should be converted to 75 ohm by using the
formulas provided by Fred (Which are also mentioned in the very good
application note in the post above).
You should design your
matching networks based on the impedances you got after the conversion
(With Zo=75 ohm).
Top
darcyrandall2004
Post subject:
Transistor Characteristic impedancePosted: Tue Feb 27, 2007 6:25 am
Colonel
Joined: Tue Feb 27, 2007 6:16 am
Posts:
46
Hello. I believe my question is related to the topic you are
discussing . I am designing a UHF (450MHz) transmitter for the sake
of interest and my own learning. The transmitter will be on a typical
PCB FR-4 board, 1.6mm thick, 1oz copper, 20mil track widths. I calculate
the characteristic impedance (Zo) to be 113 ohms. All impedance matching
will be done with components, not circuit traces. When I seek scattering
parameter information from component manufacturers, always they indicate
that the values are for a Zo of 50 ohms. I am confused as to how to
calculate the impedances of these components. Take for example a UHF
transistor, do I calculate its impedance using the Zo of my pcb being,
113 ohms, or does the silicon the transistor is made out of have a Zo
of 50 ohms and so should I use this value?
In short, does the
transistor have a Zo of 50 ohm or can I assume once placed on the PCB
the transitor has a Zo equal to my boards characteristic impedance?
I understand that a simple solution would be to design using a PCB
with a Zo of 50 ohms, but unfortunately, this is impractical.
Greatly appreciated. Darcy Randall
Top
fred47
Post subject: 50-75 OhmsPosted: Wed Feb 28, 2007 3:54
am
General
Joined: Wed Feb 22, 2006 3:51 pm
Posts:
104
Darcy,
The transistor neither has a Zo of 50 Ohms, nor
can you assume that once it's placed on the PCB, the transistor has
a Zo equal to my boards characteristic impedance. The intrinsic transistor
impedances are functions of its operating conditions: voltages and currents.
Then, the transistor is in a circuit, which will affect how
the transistor behaves.
Normally, in VHF/UHF/microwave design,
you chose your trace width to yield the desired impedance - you don't
just pick a width arbitrarily, for whatever good reason seems sufficient.
It's not hard to get a microstrip line (= PCB trace over ground
plane, for DC and Low Frequency people) with an impedance of 50 Ohms.
The good folks at www.ultracad.com have a calculator that you can use.
And our host on RF Cafe also has both formulas and calculators on this
very site.
(But you need to be careful not to mix units - mixing
mm and inches is a great way to create problems. There was a $100 million
NASA Mars probe which crashed because some people used metric, and others
used English units).
Good Luck!
Fred
Top
darcyrandall2004
Post subject: 50-75 ohmPosted: Wed Feb 28,
2007 4:43 am
Colonel
Joined: Tue Feb 27, 2007 6:16
am
Posts: 46
This is confusing. I require knowledge of the transistors
characteristic impedance, Zo, to convert the S parameters into actual
input and output impedances.
What value for the characteristic
impedance should I use then?
Cheers
Top
fred47
Post subject: 50-75 OhmPosted: Wed Feb 28, 2007 1:12 pm
General
Joined: Wed Feb 22, 2006 3:51 pm
Posts: 104
Hi Darcy,
Ahh - when you say " I require knowledge of the transistors
characteristic impedance, Zo, to convert the S parameters into actual
input and output impedances", you only missed the single point that
it's the system characteristic impedance, not the transistor's, that
you use in the conversion from S-parameters to impedances. Manufacturers
usually (=almost always!) specify 50 Ohm values. From there, you can
convert to any set of parameters you want: Z, Y, T, ABCD, H, etc - and
in fact, that's how they get the numbers in the data sheets for RF transistors.
The process many people use is:
1. Convert from S to Z. This
gives a normalized impedance.
2. Denormalize the impedance (for most
uses, that means "multiply by 50")
3. Do your design based on matching
impedances
The Smith Chart will simplify the process - you can
stay in the normalized S-parameter domain for the design, and only at
the end converting your component values to impedances and then to actual
values.
Good Luck!
Fred
Top
mhtplsh
Post subject: Posted: Wed Feb 28, 2007 11:41 pm
Captain
Joined: Wed Feb 21, 2007 12:50 pm
Posts: 18
I understand
that we can normalise the s parameters. Then design the circuit . Then
calculate the component value to desired impedance
If this is ok
then there is no need to convert s parameter from 50 to 75 ohms to design
amplifier with 75 ohm input output impedance.
Top
mhtplsh
Post subject: Posted: Sat Mar 03, 2007 8:41 am
Captain
Joined: Wed Feb 21, 2007 12:50 pm
Posts: 18
Fred47 said :
I got the answers with the help of the GPL program
Octave - makes life a lot easier than using a calculator!
I
hv downloaded the 23 mb programme. Now just guide me how u calculated
it.
In the opening screen it is like dos there is input like
octave:1>
Just waiting for ur reply,
Top
fred47
Post subject: 50-75 OhmPosted: Sat Mar 03, 2007 7:06
pm
General
Joined: Wed Feb 22, 2006 3:51 pm
Posts:
104
Hi mhtplsh!
Octave is a calculator program - you just
type in what you need.
Some examples (leaving out the prompts,
etc):
2+2<enter>
gives
4
a=2<enter>
a=2
b=3<enter>
b=3
a*b
ans=6
a*pi<enter>
ans=6.28.....
1/a <enter>
0.5
BUT the neat thing
is that it works that way with matrixes too:
octave:1> a=[1,1;2,3]<enter>
a =
1 1
2 3
octave:2> a^-1
ans =
3 -1
-2 1
So for the example, remember that the (made-up, non-actual-part)
S matrix was:
S11 = 0.5+1.0j S12 = 0.1 + 0j
S21 = 3.0 - 0.5j
S22 = 1.0 + 0.1j
I entered it into Octave like this:
octave:3> S=[0.5+1.0j,0.1+0j;3.0-0.5j, 1.0+0.1j]
and got
S
=
0.50000 + 1.00000i 0.10000 + 0.00000i
3.00000 - 0.50000i
1.00000 + 0.10000i
next, I typed
octave:4> Z=(one+S)*(1-S)^-1
Z =
0.19427 - 0.06051i -0.54459 - 0.74841i
2.34076 + 0.04140i
-0.62739 - 1.06688i
(I seem to have made a data-entry error in
my earlier posting - sorry!)
Next, denormalization is easy:
octave:5> Zdenorm=50*Z
Zdenorm =
9.7134 - 3.0255i -27.2293
- 37.4204i
117.0382 + 2.0701i -31.3694 - 53.3439i
This is
the actual impedance.
So, the point is, that Octave works the
same for a matrix (such as the S matrix) and for a single number or
variable. There are some rules which are different - you can't write
"A = B/C" if B and C are matrixes - you have to write "A = B*C^-1" like
I did above, for example.
I hope this helps get you started!
Good Luck,
Fred
Top
mhtplsh
Post subject:
Posted: Sat Mar 03, 2007 11:04 pm
Captain
Joined: Wed
Feb 21, 2007 12:50 pm
Posts: 18
Thanks fred47.
I salute ur
helping nature.
Now u hv calculated upto z 50 ohms.
But
we were needed 75 ohms.
Hence we need to do
octave:5> Zdenorm=75*Z
instead of
octave:5> Zdenorm=50*Z
Here we will get 75
ohm z parameters.
Then how to further reconvert Z to s parameters.
So i think finally we will get 75 ohm S parameters.
i got
adlabplus. In it's programme VIERPOL i fed the 50 ohm s parameters.
! f S11 S21 S12 S22
! GHz MAG ANG MAG ANG MAG ANG MAG ANG
0.10 0.79 -40 19.192 153 0.023 71 0.877 -18.
I got converted
to 75 ohms by changing 50 to 75 ohm. It asked whether i want to change
S parameter or other?
I selected S parameter & got the following
answer.
f S11 S21 S12 S22
GHz MAG ANG MAG ANG MAG ANG
MAG ANG
0.10 0.733 -67.95 24.451 141.94 0.0293 59.94 0.759 -35.33
is this ok? if yes, then this will be very easy.
ur feedback &
guidance is very important for me.
Top
fred47
Post subject: 50-75 OhmPosted: Sun Mar 04, 2007 1:29 am
General
Joined: Wed Feb 22, 2006 3:51 pm
Posts: 104
Hi mhtplsh,
My apologies - I've come down with a cold and can't think straight
- I'd be lucky to add 2 + 2 today, and I want you to have the right
answers.
I'll have to check your answers and reply later. Sorry.
Regards,
Fred
Top
mhtplsh
Post subject:
Posted: Sun Mar 04, 2007 7:09 am
Captain
Joined: Wed
Feb 21, 2007 12:50 pm
Posts: 18
My Guru Fred47,
Get well soon.
I will be waiting.
Top
mhtplsh
Post subject:
Posted: Sun Mar 04, 2007 11:58 am
Captain
Joined: Wed
Feb 21, 2007 12:50 pm
Posts: 18
Respectable Fred47
Reading
ur post once again & trying to understand inside of ur message.
u said :
To get 75 Ohm s-parameters from 50 Ohm parameters,
convert to impedance (for example, by plotting on a Smith Chart normalized
to 50 Ohms, or by formula), then convert to 75 Ohm s-parameters (for
example, by plotting on a Smith Chart normalized to 75 Ohms, or again
by formula).
A reminder about the Smith Chart: it's normalized
to a value of unity for the center point ("prime center", etc.). That
means that every impedance you plot is divided by the actual impedance.
Philip Smith did that so that you'd always be able to use the same chart.
Straight impedances, like those you get from a data sheet, aren't normalized,
so if they give a value like "10+j5 Ohms" you can normalize and plot
like always. "
What i understand :
Can we use quicksmith
for this?
U mean : the s parameter given in the datasheet r not
of 50 ohm impedance but r for unity.
So if we can then directly
select 75 ohm impedance in smith chart & can input the s parameter
from the datasheet. So they will be converted to 75 ohms?
Is this
what u mean or any other thing?
Top
fred47
Post
subject: 50-75 OhmPosted: Sun Mar 04, 2007 12:33 pm
General
Joined: Wed Feb 22, 2006 3:51 pm
Posts: 104
Hi!
I guess I didn't express myself quite clearly.
ALL s parameters
are transmission-line measurements. That means that there's ALWAYS a
connected "system" or "characteristic" impedance connected with an s
parameter - any transmission line you use will have a characteristic
impedance.
For convenience, so you don't have to buy a different
piece of paper for each impedance, the Smith Chart is normalized . That
means that you divide every value by the characteristic impedance of
the system before you plot it on the Smith Chart.
That also
means that you must multiply every value you read off a Smith Chart
by the characteristic impedance.
Here's an example: We have an
impedance of 150 + j150 Ohms. Where does that go on a Smith Chart?
It depends - let's look at it for both 50 and 75 Ohms.
Normalized
to 50 Ohms: 3 + j3
Normalized to 75 Ohms: 2 + j2
These are
at different points on the two different Smith Charts.
QuickSmith
allows you to set the characteristic impedance, and read off the denormalized
impedance from the readout for the mouse cursor.
So it's easy
to use QuickSmith to convert: set up your impedance in the circuit window
(the right window), and use either the menu or Ctrl-C to set the characteristic
impedance of the system.
You can watch the point move that way.
Good Luck!
Fred
Top
mhtplsh
Post subject:
Posted: Mon Mar 05, 2007 2:03 am
Captain
Joined: Wed
Feb 21, 2007 12:50 pm
Posts: 18
Respectable sir Fred47,
Happy
to see ur reply in spite of ur cold problem.
U mean
Normalized
to 50 Ohms: devide by 50 for 50ohms
Normalized to 75 Ohms: devide
by 75 for 75 ohms.
Now let us talk about practical example :
This will solve all the misuderstandings in our communications. Or better
for me to understand.
This is what i got in.s2p file.
! FILENAME: NE73432C.S2P VERSION: 5.0
! NEC PART NUMBER: NE73432E
DATE: 01/83
! BIAS CONDITIONS: VCE = 10V, IC = 20mA
# GHZ S MA
R 50 S11 S21 S12 S22
0.100 0.440 -101.00 19.270 122.00 0.030 65.00
0.660 -26.00
For noise figure :
TYPICAL NOISE PARAMETERS
(TA = 25°C) VCE = 10 V, IC = 20 mA
FREQ. NFOPT GA GOPT
(MHz) (dB)
(dB) MAG ANG Rn/50
500 1.40 19.5 0.26 122 0.17
Now i want
to feed input to quicksmith from the above with Chart parameter impedance
will be 75 ohm.
There r three inputs in the quicksmith.
1. S
parameters
2. Noise parameters
3. Chart parameters. : i will
put here 75 ohms.
Now just tell me what input will u put for S11,
S21, S12 & S22 & noise parameters from the above?
Top
mhtplsh
Post subject: Posted: Sat Mar 10, 2007 10:57
am
Captain
Joined: Wed Feb 21, 2007 12:50 pm
Posts:
18
I was waiting for the answer in the above matter.
But
till now no one said anything about conversion of NF data.
For noise
figure :
TYPICAL NOISE PARAMETERS (TA = 25°C) VCE = 10 V, IC = 20
mA
FREQ. NFOPT GA GOPT
(MHz) (dB) (dB) MAG ANG Rn/50
500 1.40
19.5 0.26 122 0.17
How to use/convert this for 75 ohm smithchart?
without NF data we cannot design low noise matching input circuit.
Posted 11/12/2012