

50 Ohm TO 75 Ohm  RF Cafe Forums

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.
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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 sparameters 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 sparameters (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)(1S)^1
and the scattering (s) matrix from
the impedance matrix by
S=(Z1)*(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 50Ohmdenormalized Z matrix is 50 + 25j 25.+0j
750 + 125j 175 + 250j
Now, normalize to 75 Ohms by dividing
by 75. The 75Ohmnormalized 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
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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.
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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
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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.
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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.
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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?
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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 Sparameters 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).
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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 FR4 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
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fred47
Post subject: 5075 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
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darcyrandall2004 Post subject: 5075 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
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fred47 Post subject: 5075
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 Sparameters 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 Sparameter
domain for the design, and only at the end converting your component
values to impedances and then to actual values.
Good Luck!
Fred
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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.
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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,
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fred47 Post subject: 5075 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 (madeup, nonactualpart)
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;3.00.5j, 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)*(1S)^1 Z =
0.19427  0.06051i 0.54459  0.74841i
2.34076 + 0.04140i 0.62739  1.06688i
(I seem to have made
a dataentry 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
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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.
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fred47 Post subject:
5075 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
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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.
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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 sparameters
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 sparameters (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?
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fred47
Post subject: 5075 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 transmissionline 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 CtrlC
to set the characteristic impedance of the system.
You can
watch the point move that way.
Good Luck! Fred
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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?
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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



