Adventures with an 80 Meter Loop Antenna, Part 1

Some years ago while I was dating the woman who would become my wife, I thought about setting up a station at her home in Nevada City, California, that I could use when I visited her.  Talking with friends on the morning 75 meter net, one recommended that I install a full-wave 80 meter loop.  Given her large lot and the pine trees in her back yard that could be used as supports, I thought, "Why not?"

I have a huge reel of phosphor-bronze antenna wire -- this is the same wire used to make portable wire antennas manufactured by such companies as TCI.  From it I cut a 280 foot length (very roughly 280 feet), added about 50 feet of 300 ohm ladder-line  (which was all that I had), and put it up in the back yard with pine trees supporting the four corners in a very crude diamond shape.

The ladder-line was routed under the eaves along the back of the house to where a length of RG-142 B/U 50 ohm coax protruded through a hole in the wall.  The ladder-line connected directly to the coax, and this coax then ran through the attic to my operating position.

I knew the SWR wasn't great, but my tuner could tune it and so I did not worry too much about it.  And once tuned, the loop worked very well for the 75 meter morning net, and I was even able to make DX contacts on the higher bands.  But I never looked very deeply into the antenna system's performance until I finally decided to bring my HP 3577A Vector Network Analyzer (VNA) up to the Nevada City QTH...


What SWR did my transmitter really see?

Using the HP 3577A, I made an S11 measurement at the transmitter-end of the coax in my shack.  Below is a capture over the range of 2 to 8 MHz.

Matlab vna_s11.m file provided by Dick Benson, W1QG

Here's an enlargement of the SWR plot:

Matlab SViewer.m file provided by Dick Benson, W1QG

Note that the resonant points are at 3.05 MHz, 4.64 MHz, and 7.4 MHz.  And the SWR peaks at 3.785 MHz (14.5:1) !

Ouch!  Not good -- the tuner was getting a workout !!!

Well, the obvious question now was, could I improve upon it?

Rather than guessing at how to improve the antenna, I decided to approach it analytically.  And a good starting point would be to create an EZNEC model that I could then use to experiment at optimizing the antenna system.


Creating an EZNEC  Model of the Loop:

The big problem with creating a model, though, was that the antenna was already up in the trees, and I had zero desire to lower the whole thing down to the ground so that I could measure dimensions.

But I thought I could get close enough to the actual dimensions by measuring distances on the ground between supports and by estimating heights.  Ditto for the length of the 300 ohm line.

Below is the model that I created, including the 300 ohm transmission line (which I projected horizontally from the antenna for ease of creating the model).

The EZNEC SWR plot of the impedance seen at the far end of ladder-line is:

Note resonances at 3.025, 4.7, and 7.525 MHz.

As one more check, I lugged the 3577A (and 35677A) outside (not easy, especially from a 2nd floor ham shack!) and made an S11 measurement at the end of the 300 ohm transmission line.  Here's the SWR plot of that measurement:

Matlab SViewer.m file provided by Dick Benson, W1QG

So the frequencies of the resonance dips of the S11 measurement of the actual antenna with ladder-line are very close to those of EZNEC model -- confirmation that my model was, in my opinion, good enough.

The next step -- I couldn't easily measure the impedance at the actual loop's feedpoint, but I could use my EZNEC model to estimate it by shrinking the model's transmission line down to a very short length (e.g. 0.1 feet) and calculating SWR

Very nice!  The resonances of the loop model are at 3.775 and 7.425 MHz.  Just what I would expect to see for a loop cut to be resonant in the middle of  the 80 meter band.

And here is SWR over the range of 3-30 MHz:

Note that the loop's resonances either hit or are very close to all ham bands (except 60 meters).  But note, too, that the SWR at the higher frequency resonances worsens as frequency increases.

Well, this looked very promising!  Why not remove the 300-ohm ladder line and replace it with 50 ohm coax?

I had a 67 foot length of RG-8 (Belden 8237), terminated with N connectors, back at my home in the Bay Area, so I brought it up to Nevada City.

Next I needed a way to feed the loop that used a female N connector.  Following a trip to the local hardware store...

(The B&W antenna feed at the upper right was used for temporary "proof of concept" testing, and then immediately retired!).

 Raising the loop's feedpoint, with coax attached.  Note the two 1:1 current baluns below the feedpoint.  One consists of 5 turns through two FT-240 mix 43 and two FT-240 mix 31 cores, and the other is three turns through a mix 31 clamp-core.

Measuring Performance:

The first thing I checked was the load that the transmitter would see.  I measured S11 at the transmitter end of the coax (RG-8 from antenna plus RG-142 into the shack), with the reference plane set to be the 35677A's port 1 (i.e. 1-port calibration (short, open, 50 ohm load) done at the 35677A's Port 1):

SWR at Transmitter

Matlab vna_s11.m file provided by Dick Benson, W1QG

SWR looks pretty good, but notice how the maximum SWR drops with frequency, compared to the EZNEC model of the antenna's SWR at the loop feedpoint:

Could this measured "improvement" in SWR at high frequencies be due to feed-line loss?

Fortunately, because the feed-line is now 50 ohm coax, it's pretty simple to measure the loop's feed-point impedance with the Vector Network Analyzer (VNA).  It just requires that the VNA's reference plane be set to be the end of the coax that directly connects to the loop, itself.

But to do this, I needed to:

1.  Lower the feed-point corner of the loop and disconnect the coax from the loop.  It is this end of the coax that will become the VNA's new reference plane.

2.  Perform a 1-port cal by sequentially attaching a short, an open, and a 50 ohm reference load to this end of the coax.

3.  Re-attach the coax to the loop feed-point, raise it back into the air, and do an S11 measurement on the VNA!

Here's the result:

SWR at Loop's Feed-point

Matlab vna_s11.m file provided by Dick Benson, W1QG

Compare the above SWR plot to EZNEC model:

The measured SWR minimum on 10 meters is about 4.5:1, while the EZNEC model shows 5.8:1.  So not exactly the same, but it shows that my "eyeballing" of my loop's dimensions is pretty close.

The next obvious question was...

How much power was I losing in my coax?

To calculate this I first needed to create a data file (.S2P file) of the coax cable (which consists of RG-8 and RG-142) based upon actual measurements.  This was done by measuring its four s-parameters (S11, S21, S12, S22):

Matlab vna_gui_1.m file provided by Dick Benson, W1QG

With the resultant .S2P file for the coax, and with an .S1P file for the loop antenna feedpoint impedance (generated when I made its S11 Measurement with the VNA's reference plane at the loop-end of the coax), I could then use SimSmith (by AE6TY) to calculate power-loss.

In this example, the frequency is 29 MHz, and the matching network to bring the SWR down to 1:1 is an LsCp network with an Lx of 425.5 nH and a Cp of 17.8 pF.

Total Loss is about 5 dB.  Not very good, but an improvement over the 6.8 dB of loss that would occur if there were no matching network.

Note:  to determine the matching network's values, above, I used the impedance-matching calculator at this website, as shown below:

Loss with the original Ladder-line/Coax feedline:

For a comparison of performance, I also measured the four s-parameters (S11, S21, S12, S22) of the original ladder-line plus RG-142 coax feedline.

To do this, I had to bring the ladder-line end of the feedline into the shack...

...and attach it to the network analyzer!

The SimSmith Model which includes the resultant ladder-line/coax .s2p file:

I used the same .S1P file for the antenna as I had used when calculating power-loss with the coax feedline (no need to change that file because it is data for only the loop, itself, without any feedline).

Notice that the loss at 29 MHz is 2.9 dB, after matching.  So at high frequencies the ladder-line/coax combo is better than the coax-only feedline.  (Even so, about half the power is being lost in the feedline).


Loss if add a 1:4 Impedance Transformer to Loop-end of Coax feed:

Dick, W1QG, mentioned that I should try the coax feedline with a 1:4 transformer connected to the loop at the loop feedpoint (i.e. 50 ohm port connected to coax, 200 ohm port connected to the loop, itself).

Here's the SimSmith model if an ideal, lossless, 1:4 transformer (turns ratio = 1:2)) is inserted between the antenna (L block in the diagram, below) and coax (A block in the diagram, below):

Note that the loss at 29 MHz (after matching) is now 2.5 dB.  A significant improvement over the 5 dB loss without a transformer (but still, almost half the power is lost in the feedline at 29 MHz).


Summary of Loss results:

The table, below, summarizes the loss results for the three different feedline versions (note, to save my time I skipped 160, 60, 30, and 12 meters, because I do not (yet) operate on these bands).

Conclusions:

1. The coax-only feedline beats the ladder-line/coax combination feedline on 80 through 20 meters.
2. Above 17 meters, the ladder-line/coax combo beats the coax-only feedline.
3. If we add a 1:4 transformer (in this case, lossless) to the coax-only feedline (attached at the loop), the coax-with-transformer combo beats all (although there can be an additional 0.4 to 0.5 dB loss on 80 and 40 meters, worst case). 
4. At the band edges on 10 meters, almost half the power is lost in the feedline, best case (with coax and 1:4 transformer)!

So the next task is:  build a 1:4 transformer (balun) and measure how well it performs!

Click HERE for that post!

W1QG's notes on measuring Feed Line Loss, using Matlab:

Dick is a tremendous MatLab enthusiast.  Here are his thoughts on using MatLab to measure Feed Line Loss...

The SimSmith results seemed quite reasonable,  but I have been fooled before. 

What I wanted was an alternative method, and preferably one that did not require creating an LC matching network for each frequency of interest.   Now, SimSmith may well do this, but it would require some digging.

I know MATLAB will do it, and it is a good check on the SimSmith results. 

The key is the function called powergain: 

(https://www.mathworks.com/help/rf/ug/powergain.html)

Gp gives the powergain (note that it will be a LOSS for this work) given the:

  1) s_parameters of the system (Coax in this case), including Zo that the S_parameters are based on.

  2) Zl= the load impedance which is the antenna.

Note that Gp does NOT incorporate the source impedance.

The neat thing is the Gp result is what you would get if you conjugately match the input of the S parameter system.  So creating the little LC match for each freq (a la SimSmith) is not needed. 

Now, for the sake of completeness, and because it is trivial to do, Gt and Ga were also calculated.   

Ga is what you would get if you just look at the line loss with Zs=50 ohms. Note that there is no Antenna information.

And Gt is what you get if you have a 50 ohm Zs, and the Antenna as a the load.   

Here is the big picture.

SimSmith predicts 9.64 dB loss at 5.36 MHz,  5.38 dB at 28.01 MHz, and 4.74 dB at 28.11 MHz.

The small discrepancy comes from the tiny but finite loss of the LC and inexact freq match of the 28.04 vs 28.01.  

Here is a close up of 20 M:

Another interesting view is to plot Gp , Ga , and the Antenna SWR:

No surpise: minimum loss at minimum SWR.

The only eye opener is how large the Feed Line loss can be a low frequencies where the *measured* antenna SWR goes through the roof. 

For further entertainment, the MATLAB "Publish" feature generated this html "report", and it is attached as well.

Contents

§                      Read the 3 relevent s-parameter files

§                      First, a sanity check on the coax and antenna measurements.

§                      Compare measured SWR with Predicted SWR

§                      Compute Power Gain (it will be a loss!) of the (Coax) Feed Line to the Antenna Load

§                      Another interesting plot would be the Antenna SWR along with Gp.

% Predicting Feed Line Loss with MATLAB

% Dick Benson

clc

clear all

close all

Read the 3 relevent s-parameter files

These are actual measurement data from K6JCA Loop Antenna

path=[pwd,'\'];

s= '180508 Nevada City Loop, Coax Fed,  SOL CAL, 2-30MHz.s1p'; 

[Antenna_Obj,Antenna_Notes,Antenna_State]         = spar_read(path,s);

s= '180508 Nevada City Loop Coax.s2p';

[Coax_Obj,Coax_Notes,Coax_State]                  = spar_read(path,s);

s= '180518 Nevada City Loop, Coax Fed,  Two Choke baluns, 2-30MHz.s1p';

[Composite_Obj,Composite_Notes,Composite_State]   = spar_read(path,s);

First, a sanity check on the coax and antenna measurements.

SWR will be the comparison metric.

Zo = Antenna_Obj.Z0;            % assumed 50 ohms for all s-parameter files

FreqMHz= Antenna_Obj.Freq*1e-6; % AND assume Freq Vector is the same for all as well.

Z_Antenna = gamma2z(Antenna_Obj.S_Parameters,Zo);

Gamma_Coax_Plus_Antenna= gammain(Coax_Obj.S_Parameters,Zo,Z_Antenna);

Compare measured SWR with Predicted SWR

SWR_Measured   = vswr( squeeze(Composite_Obj.S_Parameters));

SWR_Antenna    = vswr( squeeze(Antenna_Obj.S_Parameters));

SWR_Predicted  = vswr(Gamma_Coax_Plus_Antenna);

figure

plot(FreqMHz,SWR_Measured,FreqMHz,SWR_Predicted)

legend('Measured Composite SWR','Predicted SWR by Separate Coax and Antenna Meas.')

title('Compare Prediction of Separate Coax, Antenna, to Single Composite SWR ');

xlabel('Freq in MHz');

ylabel('SWR');

text(7,12,'The agreement is VERY GOOD!')

figure

h_lines = semilogy(FreqMHz,SWR_Measured,FreqMHz,SWR_Predicted,FreqMHz,SWR_Antenna);

set(h_lines(3),'Color',[1 0 0],'Linewidth',1);

legend('Measured Composite','Predicted by Separate Coax and Antenna Meas.','Actual Antenna SWR')

title('Compare True SWR at the Antenna, to SWR at End of Feedline');

xlabel('Freq in MHz');

ylabel('SWR')

grid on

grid minor

text(7,130,['The actual antenna SWR is huge compared to what is ',char(10),...

            ' observed at the end of the coax.',char(10),'       (NOTE:log Y axis)'])

Compute Power Gain (it will be a loss!) of the (Coax) Feed Line to the Antenna Load

Zs=Zo;

 Ga    = powergain(Coax_Obj.S_Parameters,Zo,Zs,'Ga');           % Just Feed Line loss in the matched case.

 Gt    = powergain(Coax_Obj.S_Parameters,Zo,Zs,Z_Antenna,'Gt'); % System loss with 50 ohm Zsource.

 Gp    = powergain(Coax_Obj.S_Parameters,Zo,Z_Antenna,'Gp');    % This is the one we want !

 % Note that Gp has no dependence on the source (Zs) impedance. It only depends on the

 % S-Parameters (which need to have Zo spec'd) and the Load impedance (the

 % Antenna)

 %

figure

h_lines= plot(FreqMHz,-10*log10(abs(Ga)),FreqMHz,-10*log10(abs(Gt)),FreqMHz,-10*log10(abs(Gp)));

set(h_lines(1),'Linewidth',1,'Color',[1 0 0]);

set(h_lines(2),'Linewidth',1,'Color',[0 0 1]);

set(h_lines(3),'Linewidth',2,'Color',[0 1 0]);

xlabel('Freq in MHz');

ylabel('Loss in dB');

legend('Ga','Gt','Gp');

grid on

grid minor

text (7,16,['Ga=Available Power Gain',char(10),'Gt= Transducer Gain',char(10),'Gp=*Operating Power Gain*']);

Another interesting plot would be the Antenna SWR along with Gp.

figure

[hAx,hLine1,hLine2]=plotyy(FreqMHz,[-10*log10(Gp),-10*log10(Ga)],FreqMHz,SWR_Antenna);

set(hLine1(1),'Color',[0 1 0],'Linewidth',2);

set(hLine1(2),'Color',[1 0 0],'Linewidth',2);

set(hLine2,'Color',[0 0 1],'Linewidth',2);

legend('Operating Loss in dB','Matched Line Loss','Antenna SWR')

xlabel('Freq in MHz');

grid on

grid minor

ylabel(hAx(1),'Loss in dB');

ylabel(hAx(2),'Antenna SWR');

title('Loss and Antenna SWR vs Freq');

Published with MATLAB® R2015a

That's it for this post!

Analysis of my loop and its balun continue in the following blog posts...

My Balun (and 80-Meter Loop) posts:

80 Meter Loop, Part 1:  http://k6jca.blogspot.com/2018/05/adventures-with-80-meter-loop-antenna.html

80 Meter Loop, Part 2:  http://k6jca.blogspot.com/2018/05/adventures-with-80-meter-loop-antenna_30.html

Balun Power Dissipation:  http://k6jca.blogspot.com/2018/06/common-mode-chokes-baluns-power.html

Notes on 1:1 Baluns:  http://k6jca.blogspot.com/2018/06/transmit-common-mode-chokes-11-current.html

Notes on Common-Mode Currents:  http://k6jca.blogspot.com/2018/07/thoughts-and-notes-common-mode-current.html

Y21 Method of Measuring Common-Mode Impedance:  https://k6jca.blogspot.com/2020/07/the-y21-method-of-measuring-common-mode.html

A 3-Port Method for Characterizing Baluns:  http://k6jca.blogspot.com/2020/06/another-method-to-characterize-baluns.html

MATLAB Scripts for Plotting VNA Data:

Dick Benson's MATLAB scripts for capturing VNA data (e.g. from an HP 8753x) and displaying it (that I use above) can be downloaded from his page in the MathWorks file exchange section:  Dick Benson MATLAB files

Standard Caveat:

Either I or Dick Benson (W1QG) might have made a mistake in our designs, equations, schematics, models, etc.  If anything looks confusing or wrong to you, please feel free to comment below or send me an email.

Also, I will note:

This design and any associated information is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

"Tandem Match" Transformers and Calculating their Maximum Flux Density

This blog post discusses the "Tandem Match" directional-coupler topology and how to calculate the flux-density in the cores of this directional-coupler's two transformers (voltage-sense transformer and current-sense transformer).

(Note:  In the circuit above the values of the two resistors labeled "R" should be the same as the characteristic-impedance of the transmission-line system being analyzed.  E.g. each R should be 50 ohms if the transmission-lines are 50 ohms.  Also, the load should really be represented by a complex impedance, "Zload".  I am using a resistance "Rload" for simplicity.  And for the same reason I am assuming ideal transformers.)

Why is calculating the cores' flux-density important?

Selecting toroid cores for a Tandem-Match directional coupler depends in large part upon the maximum anticipated flux-density in each transformer's core (the core for the current-sense transformer and the core for the voltage-sense transformer).  Too small of a core and it might burn up from excessive core loss, and too large a core means you are probably wasting money and certainly wasting space.

(In addition to heating failures, cores can also fail from saturation.  But the saturation flux density is significantly higher than the flux-density limit for heating.  Never the less, it should be verified, too).

An important note!  Every tandem-match coupler implementation I've seen uses the same core size for the current-sense transformer and for the voltage-sense transformer.  This need not be!  In fact, the current-sense transformer's core can be significantly smaller than the voltage-sense transformer's core, as I will explain later in this post.

What are the flux-density limits?

With respect to core heating, iron-powder cores and ferrite cores have, essentially, the same maximum flux limits versus frequency (these are the limits that the DL5SWB Mini Ring Core Calculator uses and which are based on (and interpolated from) Amidon's recommendations.):

But cores can also saturate.  Per Amidon, saturation is a secondary cause of core failure, and the saturation flux-density is typically 2000 gauss for ferrite cores and 5000 gauss for powdered-iron cores.

So the saturation flux-density limit is significantly higher than the "core-heating" maximum flux density limits shown in the table, above.

Calculating Flux Density:

Flux density is a function of the voltage across the "driven winding" of a transformer and follows the relationship below:

(Flux-density equation derivation can be found here.  Note that the 10^8 factor in the numerator is  because Ae is in cm^2, not m^2, and we are calculating Gauss, not Teslas (1 gauss = 0.0001 tesla).)

Bmax = (|Vmax| * 10^8) / (4.44 * f * N * Ae) gauss

Note: when calculating flux-density for core-saturation purposes, I would recommend using Vpk rather than Vrms for voltage in the Bmax equation.  In other words, for saturation calculations:

Bmax(saturation) = (Vpk * 10^8)/(4.44 * f * N * Ae)

And Vpk should be calculated under worst-case conditions.

Determining the voltage:

The voltage (Vrms or Vpk in the Bmax equations, above) is easily determined for the voltage-sense transformer -- the voltage across its driven-winding is simply the voltage seen at the directional-coupler's output port.  In the circuit, above, it is Vo.

But the voltage across the "driven winding" of the current-sense transformer isn't as obvious.  However, it can be derived by "reflecting" the impedance connected to the current-sense transformer's n-turn secondary into the transformer's primary, and then calculating the primary's voltage by multiplying the primary's current by this reflected impedance.

Let's derive this reflected impedance...


Deriving the Reflected-impedance of the Voltage-sense Transformer:

Below is a model of the "Tandem Match" directional coupler.  I am assuming that the coupled-inductors are ideal transformers.  And I assume that the load is at the output port of the directional-coupler, so that I can used lumped-element analysis.

I'll use Loop-analysis.  Below I define the loops I will use:

Here are the equations for these four loops:

   Loop 1:  Vi - Va - Vo = 0

   Loop 2:  Va*n - R*(i1/n + i4*n) = 0

   Loop 3:  Vo/n - i4*n*R - R*(i4*n + i1/n) = 0

   Loop 4:  -Vo + Rload*(i1 - i4) = 0


Deriving the Reflected-impedance of the Current-sense Transformer:

Let's rearrange loop 4 to be an expression for Vo:

Vo = Rload*(i1 - i4)

This equation for Vo can then be substituted into the loop 3 equation's Vo term.  We can then express i4 in terms of i1:

i4 = i1*(Rload - R) / (2*R*(n^2) + Rload)

Substituting this equation for i4 into the loop 2 equation and rearrainging, we can derive the current-sense transformer's primary impedance (reflected from the secondary):

Va/i1 = R/(n^2) + R*(Rload - R)/(2*R*(n^2) + Rload)

The primary's impedance is a function of Rload, R, and n.  Not a simple relationship, is it?

Flux density is simply the current passing through the 1-turn primary winding of this transformer multiplied by this "reflected resistance:"

Bmax = (Imax * (Va/i1) * 10^8) / (4.44 * f * Ae) gauss

Note that 'N' (the number of turns of the current-sense transformer primary) in the original Bmax equation has been set to one (representing the current-sense transformer primary's single turn and so it does not appear in this equation..

Now that we have this equation...


How Does Core Flux-Density Vary with SWR?

As SWR increases from the ideal 1:1, a voltage standing wave and a current standing wave will form on the line.

The directional-coupler might be placed in the transmission line at a point where the voltage of the voltage standing wave is maximum, or where the current of the current standing wave is maximum.  So it is these maximum values that I use as Vmax and Imax when calculating the flux density of these two transformers.

Let's take an example.

Let's say that I'd like to design my directional-coupler so that it could run without overheating on a transmission line where the SWR is 3:1, worst-case, and 200 watts is being dissipated by the load.

To simplify calculations, I'll assume that the load is resistive and that the directional coupler is placed at the load -- this is where the voltage maximum will occur of the load resistance is greater than the transmission line's Zo, and it is where the current maximum will occur if the load resistance is less than the transmission line's Zo.

(Note:  you don't need to assume that the directional coupler is placed at the load to calculate Vmax and Imax.  There is a bit more math, but it isn't difficult. See this blog post:  Useful Transmission Line Equations))

For a given SWR, I will use two load resistances -- the resistance that gives me Vmax, and the resistance that gives me Imax.  For example, for a 3:1 SWR and a transmission line Zo of 50 ohms, these resistances are 150 ohms and 16.67 ohms, respectively.

Given the power being dissipated by the load and the load's resistance, calculating the current and voltage at the directional coupler is straightforward.  These values are then used to calculate the transformer flux densities.

The table below shows the flux densities if the transformer core were an FT-50 Mix 43 core, given load power to be 200 watts and a transformer turns-ratio of 24:1.

At 3.5 MHz the maximum flux density (to prevent overheating) should be limited to 80 Gauss.  You can see that at all SWRs the flux density of the voltage-sense transformer is well above this value.  So the Mix 43 FT-50 core is not a core I would want to use for my voltage-sense transformer.

On the other hand, the flux density of the current-sense transformer is well below the 80 Gauss limit for my range of SWRs.  So this core would be OK to use for the current-sense transformer.

(Note, too, that the current-sense transformer's flux-density only depends upon SWR, not the value of the load resistance at that SWR -- it is the same for the maximum resistance and the minimum resistance loads that have the same SWR.)

What core could I use for my voltage-sense transformer? 

I have a handful of 2643625002 cores in my junkbox.  How would they perform?  Below is a table showing their flux densities versus SWR for this core:

As you can see, the flux density is only greater than the 3.5 MHz 80 Gauss limit when the load resistance is greater than about 130 ohms (SWR of 2.6:1).  So, although it doesn't quite meet my design goal of handling a 3:1 SWR all day long, it's close enough that I would probably change my design goal to be the ability to handle a  2.6:1 SWR all day long.

Calculating the Current in the Voltage-sense Transformer's Primary:

If calculating the heating of the wires used to wind the voltage-sense transformer, we need to know the current flowing through these windings.

Let's assume that the resistance reflected by the voltage-sense transformer's one-turn secondary into its primary is much less than the inductive reactance of the primary.  In other words, the primary's current essentially flows through the resistance.

From the loop equation, above, we can derive an equation for this current:

i4 = Vload * (Rload - R) / (R*Rload*(2*(n^2) + 1))

Where 'n' is the turns ratio (e.g. 24) and R is the characteristic impedance of the transmission line (e.g. 50 ohms).

Note a couple of things about this equation:

1.  If Rload equals R (i.e. if Rload equals 50 ohms), no current flows.  I.e. no current is flowing in the 24-turn primary, and thus no current is flowing in the 1-turn secondary of the voltage sense transformer.

2.  If Rload is less than R, then i4 will be negative.  This just means that the current is flowing in the opposite direction.  

3.  The current through the transformer secondary will be (n*i4).

LTSpice Verification:

To verify my derivations, I created the following LTSpice model (with transformer turns ratio assumed to be 16:1):

The LTSpice simulation voltage results (versus Rload and referenced to Vin) are below, in dB:

I then used Excel and my hand-derived equations to calculate the same voltages (shown in the yellow columns, below):

Note that the Va of this spreadsheet is the same as "Vin-Vo" of the simulation.  If you compare the simulation results to the results based upon my derived equations, you will see that they are the same.

Additional notes on the spreadsheet based upon my derived equations:

1.  I had to derive one additional equation to calculate the results above:

Rx = Vo/i1 = (R*Rload*(1+2*(n^2))/(2*R*(n^2) + Rload)

2.  "Ra" in the spreadsheet is simply Va/i1, the formula for which appears earlier in this post.

Conclusion:

When designing a "Tandem-match" directional coupler, the voltage-sense and current-sense transformer cores should each be sized appropriately for their respective anticipated maximum flux-density with respect to heating (calculate assuming long-term average-power usage) and with respect to saturation (calculate assuming peak-power (and thus peak-voltage) under worst-case conditions usage).  For more information (and an example) on determining the conditions to use when calculating these cases, see part 5 of my Automatic Antenna Tuner posts for the conditions I had used.

The flux-density in each transformer can be calculated as follows:

Voltage-sense transformer flux-density:

Bmax = (|Vmax| * 10^8) / (4.44 * f * N * Ae) gauss

where |Vmax| is the maximum voltage on the transmission line for the maximum SWR, at max power, that I would expect to see.

Current-sense transformer flux-density:

Bmax = ((|Imax| * Rprimary)) * 10^8) / (4.44 * f * N(primary) * Ae) gauss

where Rprimary of the current sense transformer is:

Rprimary = R/(n^2) + R*(Rload - R)/(2*R*(n^2) + Rload)

and where:

• N(primary) is the turns-count of the primary winding, and equals1.
• R equals the Zo of the transmission line (e.g. 50 ohms).
• n is the transformer turns-ratio (e.g. 24).

Note that Vmax and i1 in the equations above should be RMS values when calculating heating flux-density and peak-voltage values (i.e. 1.414 times the RMS value) when calculating saturation flux-density.

And a final note:  I've ignored effects such as winding inductances for the calculations in this post, assuming, for example, that their impedances are sufficiently greater than any resistances in parallel with them.  But a good designer will check and verify these, too.


Links to my Directional Coupler blog posts:

Notes on the Bruene Coupler, Part 2

Notes on the Bruene Coupler, Part 1

Notes on HF Directional Couplers (Tandem Match)

Building an HF Directional Coupler

Notes on the Bird Wattmeter

Notes on the Monimatch

Notes on the Twin-lead "Twin-Lamp" SWR Indicator

Calculating Flux Density in Tandem-Match Transformers


And some related links from my Auto-Tuner and my HF PA posts:

Auto Tuner, Part 5:  Directional Coupler Design

Auto Tuner, Part 6:  Notes on Match Detection

Auto Tuner, Part 8:  The Build, Phase 2 (Integration of Match Detection)

HF PA, Part 5: T/R Switching and Output Directional Coupler


Standard Caveat:

I might have made a mistake in my code, designs, equations, schematics, models, etc.  If anything looks confusing or wrong to you, please feel free to comment below or send me an email.

Also, I will note:

This information is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Counterfeit LM2596 Regulator Boards

Recently Dick Benson, W1QG, mentioned to me that he had ordered 10 LM2596 adjustable voltage regulator boards from eBay for the incredibly low price of $10.99, including shipping.

Well, this seemed like a great deal to me, too!  So I also placed an order for 10 boards.

Dick received his boards while mine were still in transit.  While testing them, he discovered that the switching frequency was 50 KHz, not the 150 KHz specified for an LM2596 switching regulator.

Hmmm...could the regulators on these boards actually be LM2576 regulators that have been relabeled as LM2596 regulators?  Or (and probably more likely) are these regulators poorly implemented copies of the LM2576 regulator that have been relabeled as LM2596 parts and that might fail later in a disastrous way?  Without looking at the die itself and comparing it with the die of a true LM2576, there's no way for me to know.


Measurements, Original Board:

My boards arrived and I ran some tests of my own...

Below is one of the 10 boards in my test setup.  I configured the setup so that the output voltage would be 5V with an output current of 1 amp (i.e. 5 ohm load resistor).  The input voltage is 12V:

(Click on image to enlarge)

(The 10 watt, 5 ohm resistor will be dissipating 5 watts and thus gets very hot, so I placed it in a clay flower-pot saucer.)

Measurements:

    o Measured Input Current: 0.511A

    o Measured Output Voltage:  5.00V

    o Calculated Input Power:  12.0 * 0.511 = 6.13W

    o Calculated Output Power: (5.00 ^ 2)/5 = 5.0 W

    o Calculated Efficiency: 5.0/6.13 = 82%

The measured Output Ripple:

    o  Amplitude:  234 mVpp

    o  Frequency:   52.8 KHz  -- This part cannot be an LM2596!

See oscilloscope capture, below:

(Click on image to enlarge)

Measurements, Counterfeit regulator replaced with LM2596:

I replaced the fake LM2596 on one of the boards with a real LM2596:

Measurements:

    o Measured Input Current: 0.508A

    o Measured Output Voltage:  4.99V

    o Calculated Input Power:  12.0 * 0.508 = 6.1W

    o Calculated Output Power: (4.99 ^ 2)/5 = 4.98 W

    o Calculated Efficiency: 4.98/6.1 = 82%

The measured Output Ripple:

    o  Amplitude:  102 mVpp
    o  Frequency:  147 KHz

Dick, W1QG, had reported poor ripple performance on his boards due to high-ESR of the output caps.  I thought I'd do some experiments of my own with some capacitors I had on hand.

First...

Replace original 220uF, 35V electrolytic output cap with a 100uF, 10V tantalum cap:

Measurements:

    o Measured Input Current: 0.500A

    o Measured Output Voltage:  4.96V

    o Calculated Input Power:  12.0 * 0.500 = 6.0W

    o Calculated Output Power: (4.96 ^ 2)/5 = 4.92 W

    o Calculated Efficiency: 4.92/6.0 = 82%

The measured Output Ripple:

    o  Amplitude:  54.4 mVpp
    o  Frequency:  146 KHz

Next...

Replace the output cap with a 330uF, 10V, 100 milliohm ESR tantalum cap:

Measurements:

    o Measured Input Current: 0.501A

    o Measured Output Voltage:  4.96V

    o Calculated Input Power:  12.0 * 0.501 = 6.01 W

    o Calculated Output Power: (4.96 ^ 2)/5 = 4.92 W

    o Calculated Efficiency: 4.92/6.01 = 82%

The measured Output Ripple:

    o  Amplitude:  52.8 mVpp
    o  Frequency:  149 KHz  

Note that the ripple amplitude is essentially the same for the 100uF and 330uF tantalum capacitors!  This implies that the ripple current amplitude, for these caps, is probably due to ESR, not capacitance value.

And finally, I thought I'd try a through-hole cap...

Replace the output cap with a 220uF, 63V Elena electrolytic cap:

Measurements:

    o Measured Input Current: 0.501A

    o Measured Output Voltage:  4.96V

    o Calculated Input Power:  12.0 * 0.501 = 6.01 W

    o Calculated Output Power: (4.96 ^ 2)/5 = 4.92 W

    o Calculated Efficiency: 4.92/6.01 = 82%

The measured Output Ripple:

    o  Amplitude:  83.2 mVpp
    o  Frequency:  146 KHz  

Note that the ripple is worse!  

Replacing the potentiometer with a resistor:

Another modification I made was to replace the pot with a fixed resistor.  Pots fail, and when they fail they will usually fail open.  If this happens on this board, the regulator board's output voltage will go to its maximum value, probably frying circuitry downstream.

So I'd much rather replace the potentiometer time-bomb with a resistor!  Fortunately, this is easy to do.

If you remove the potentiometer, you will see under it pads for an SMD resistor.  Simply load the correct value of resistor onto these pads and, voila, you will have a fixed-voltage regulator board!

If you look at the LM2596 datasheet (section 9.2.2.2.2) and compare it to the regulator board, you will see that the datasheet's R1 is already stuffed (with 330 ohms in my case) and that the SMD pads under the potentiometer are for R2.

With an R1 of 330 ohms, then, for a 5V output, R2 should be 1K ohms.

Here's the board I modified to be 5V fixed output:

(This board has also been modified with the correct LM2596 regulator and a 100uF tantalum output cap).

W1QG Measurements:

Dick also ran his own tests on his boards.  Here are his results:

As I mentioned, the ESR of both the input and output caps is substantial.

  

The PCB I used was probably one of the worst, but I cannot confirm this.

       

This 220 uF @ 35V output cap has an ESR of 0.57 ohms, and its actual C is 173 uF (not shown):

       

 In all cases, the input voltage was 12V, and the output was set to 5V into a 5 ohm load.

      

This output cap was replaced with a tantalum rated at 220uF, 10 V:

       

 The ESR is 0.058 ohms which is about 1/10th that of the "stock" version. 

Also note that it's physical size is about 3 to 4X bigger with the voltage rating of only 10V.  Its capacitance was 208 uF. 

The stock cap was replaced with this tantalum, and another measurement made:

    

     

For the last measurement, the counterfeit IC  (LM2576) was replaced with the ON Semi LM2596.

Results:

      

        

Changing to the low ESR Tantalum provided a 13.9 dB reduction in the pp level.

         

Then changing the IC to a "real" LM2596 reduced the pp ripple by 21 dB from the original. 

Other Notes:

The LM2596 datasheet contains a wealth of information regarding component selection.  It is well worth the read.

In my tests the board itself was dissipating about 1 watt of power (for a 1 amp output at 5v and and input voltage of 12v).  The board gets noticeably warm!  If dissipating more power (and perhaps even at this power), I would recommend heat-sinking the board.  To accomplish this, I would scrap away the solder-mask on the back side of the board (under the LM2596's tab) and solder a heatsink to this area (copper would be a great choice for heatsink material).

Here's a schematic I've drawn of the boards that I received from eBay:

I checked the component values (but not voltage ratings) on one of the ten boards I received, and the values are all within 10 to 20% of the values shown on the schematic.

Specifically:

  o  The input 100uF cap measured to be 87uF, ESR of 0.66 ohms.

  o  The output 220uF cap measured to be 200uF, ESR of 0.28 ohms.

  o  The 100nF caps measured to be 117nF and 120nF.

  o  The 47uH inductor measured to be 45uH.

All measurements were made at 1 KHz using a GenRad 1657 Digibridge.

Standard Caveat:

I might have made a mistake in my code, designs, equations, schematics, models, etc.  If anything looks confusing or wrong to you, please feel free to comment below or send me an email.

Also, I will note:

This information is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.