Using equal value resistors to make 50 ohms compared to other options

[cncjerry]

Question for ya:  I was playing around with a parallel resistor calculator that selects resistors to hit a specific value within a specified percentage.  I wasn't thinking and put in 50 ohms as a test thinking it would spit out 100 ohms in parallel with 100 ohms making 50 ohms.  But it displayed 75 ohms in parallel with 150 ohms which is a combination I haven't used in reflection bridges and other devices that need an accurate 50 ohm termination.

So that's the question, if I run out of 100 ohm resistors would there be some obscure RF related reason I wouldn't want to use 75 in parallel with 150 instead of 100 and 100?

Thanks

[Teuobk]

The frequency response of the different values could be different, particularly at 1+ GHz.

See, for example, this white paper from Vishay: http://www.vishay.com/docs/60107/freqresp.pdf

[cncjerry]

Having a pretty accurate VNA, I am going to test the two setups.  I don't know why I didn't think to use all the test equipment I've acquired.  What the heck is it good for?  Most of the time I am just cleaning and calibrating it. ha!

I'll report back in a few days.  I'll have to use perfectly cut leads if I use thru-hole resistors because I know I can measure the inductance difference depending on lead length and position above the board.

[bitseeker]

Very interesting question. Looking forward to your findings, Jerry.

Glad to see you've found a use for all your gear.

[cncjerry]

All passives have both inductance and capacitance.  The question will be what is coming from the resistive material vs the lead length, soldering, etc.

Yes, bitseeker, my equipment will feel useful for once.

[alm]

I would expect there to be a difference. Obviously there would be no difference at DC (apart from maximum power dissipation), so the only thing to worry about is parasitics. With resistor values within a decade I would expect their construction to be quite similar, and the parasitics would be dominated by the package and PCB. Assuming these low value resistors are mostly inductive at high frequencies, you would have two parallel LRL combinations:

Code: [Select]


   +-[L]---[100R]---[L]-+
---+                    +---
   +-[L]---[100R]---[L]-+

   +-[L]---[150R]---[L]-+
---+                    +---
   +-[L]---[ 75R]---[L]-+
You could add in capacitance between the nodes, but I do not think that would make much difference. The first combination would obviously have the lowest reactance. The value of L would obviously quite low for chip resistors with short, reasonably wide PCB traces, so the difference would probably only show up at hundreds of MHz if not GHz. You'd be talking fractions of a nH and pF here. Slightly more with leaded resistors.

Now whether this difference is enough to worry about and not swamped by other factors like a resistor not exactly centered on the pads or a 1mm difference in lead length, that is something real measurements might point out . I would think you might need multiple samples of each combination to rule out small difference in construction.

[cncjerry]

Well, from 1 to 60 Mhz the only difference is the parallel value of the resistors.  I hadn't had my N2PK VNA out in a while and it has proven to be more accurate than my scaler systems with tracking generators so I thought I would give it a try with this problem.  So I made a little test circuit using a protoboard and two SMA connectors and calibrated it for a transmission comparison.  I used 2 x 100ohm resistors that in parallel were 49.964ohms and 1 x 75 and 1 x 150 that in parallel were 50.367ohms.

I ran the test and the traces speaks for themselves.  The only difference you can see at this limited frequency range is due to the difference in parallel resistance with the lower trace being the higher parallel combination.  You can see the trace is far from flat, varying about .5db over the range.  I started thinking I would see different peaks with the two combinations but not at this frequency.  The next time I run this test I will take it out to 3Ghz to see if there is a noticeable difference in frequency response.

[alm]

No obvious differences up to 60 MHz makes sense to me. At these frequencies the parasitics' contributions to the impedance will likely be very minor. If the difference between the parallel resistors were larger (e.g. 470R // 56R), I would expect the effect to be stronger, since the reactance in series with the 56 Ohm resistor would dominate (perform closer to a single 50 Ohm resistor than two 100 Ohm resistors). But even then you likely would need to go much higher in frequency.

[spudboy488]

Power (heating) will be different for the 75/150 combination. Two 100s will split the power evenly. None of this may come into play and will depend on the circuit they are used in but it can be a difference maker in high power use.
 

[cncjerry]

I'm thinking of low power as in reflection bridges up to 1Ghz.  I'm going to keep testing.

[rfbroadband]

0402, 0603, 0805 etc resistors have different parasitic Ls and Cs as a function of their physical size. You can build a close to perfect 50Ohm resistor by using two 0402 100 Ohms resistors in parallel. The parasitic L,C will provide you with a constant impedance of 50 Ohm (vs freq) of up to almost 20GHz.

[Bud]

I've seen a few times in different Agileng papers they recommending two 0603 100 Ohm resistors in parallel.

[Teuobk]

I decided to give this a try too, so I got some Molex surface-mount SMA connectors, a bunch of 0805 and 0603 resistors, and my new-to-me HP 8714ES VNA.

For calibration, I used a homemade OSL cal kit using the same Molex female SMA connectors and two 0603 1% Yageo 100 ohm resistors soldered in parallel to what would be the board side of those connectors. Generally, the IN3OTD approach.

For the unequal resistors, I used 51 ohm and 2700 ohm (nominal) resistors. I picked from sets of 6 of each of them for the match that would be closest to a DC resistance of 50 ohms when in parallel.

I did the experiment several times with each of the sizes of resistors and got basically the same results, so I'll describe only the 0805 case in detail here.

The 51 ohm resistor was measured to be 51.04 ohms, and the 2700 ohm resistor was measured to be 2662 ohms. In parallel, once soldered to the SMA connector, the DC resistance was 50.06 ohms.

I also made a nearly identical setup with 0805 100 ohm resistors in parallel. Its DC resistance was 50.05 ohms.

And now, the results.

Here's the log magnitude (Green = 51||2k7, yellow = 100||100):


The impedance magnitude (Green = 51||2k7, yellow = 100||100):


The Smith chart (Green = 51||2k7, yellow = 100||100):


The Smith chart zoomed in (Green = 51||2k7, yellow = 100||100):


The Smith chart with some markers, but just for the 51||2k7 case (Yellow = 51||2k7):


I was a bit surprised by the divergence -- particularly the fact that the impedance magnitude went up with frequency instead of down -- so I ran this many times, using different SMA connectors, different resistors (but the same values), and so on. The results varied very slightly from setup to setup, but they were always like what I described above in general terms.

I mean, I was expecting the behavior with the unequal resistors to be a little different, but not *this* different. I'm still relatively new to the world of VNAs, so if it looks/sounds like I was doing something wrong in my experimental setup, I'd like to hear about it.

Anyhow, just thought that was interesting. There is indeed a difference. 

[Co6aka]

I was expecting the behavior with the unequal resistors to be a little different, but not *this* different.

Seems reasonable to me; the "higher" value resistor starts to look like an inductor (then parallel L/C.) Rule of thumb (which I might as well have been born with because I don't remember where my thumb came from) is to use the lowest value resistors needed to achieve the desired resulting resistance. I didn't look up the data sheet for the resistors you used; are they thin film or thick film? Also, if you can get some MELF package parts give those a try. I've gotten good results with two 100-Ohm MELF in parallel.

[Teuobk]

I didn't look up the data sheet for the resistors you used; are they thin film or thick film? Also, if you can get some MELF package parts give those a try. I've gotten good results with two 100-Ohm MELF in parallel.

Unfortunately, I don't have the datasheets for the resistors. They were all part of a grab bag, and they were cheap, so I suspect they were thick-film. It's entirely possible that they were different types, which would obviously spoil these results. Then again, I ran the tests a few different ways, with both 0603 and 0805 parts, and the results were always generally the same as the ones I described in detail above. The reference 0603 resistors used as the 50 ohm load during calibration were 0603 thin-film 1% Yageo parts, each 100 ohms and soldered in parallel. The parallel 100 ohm resistors shown in the dual-trace comparisons above were from the same group of resistors as the 51 and 2k7 resistors, and were probably thick-film.

The next time I make a Digikey order, I might buy some more high-grade thin-film resistors of the appropriate sizes to make this extra-rigorous. If other people have more 51 and 2k7 chip resistors around, plus a network analyzer, I'd be curious to see if my results can be replicated.