## 50 Ohm TO 75 Ohm - RF Cafe Forums
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Below are all of the forum threads, including all 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
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