Experimenting with Directional Couplers

Experimenting with Directional Couplers

Recently, I have been obsessed with home-brewing  RF/microwave test equipment. There is something so enthralling about building something that would help you build something else.

Perhaps the most important RF instrument is the Vector Network Analyser. As the name suggests, a VNA can characterise a DUT. This is done in the form of Scattering Parameters. For a 2 port device there are:

Image result for S parameters
source: http://edadocs.software.keysight.com/display/sv201007/Theory+of+Operation

More on this later, in the VNA build posts. For now we focus on measuring reflected power or S11/S22. How exactly, does one measure these? Thinking about a general transmission line, we know at any given moment there is a forward and reflected wave travelling, we need a device that only measures/responds to the reflected wave. As usual, there are many ways to do this, but the result is a device typically called a directional coupler. For example, a micro strip approach would consist of 2 coupled lines:

Source:https://www.everythingrf.com/rf-calculators/directional-coupler-calculator

Such a device is only really suitable for high frequency (>few GHz), and requires careful construction using specialised PCB laminates. Another, more broadband approach (suited all the way down to DC) is to employ a standard Wheatstone bridge:

Source: Agilent

Although the “mechanism” for detecting the reflected wave is totally different, the detector output is still proportional to the DUTs reflection coefficient as required. All we are simply doing here is measuring how well our DUT input impedance matches our reference impedance (usually 50 Ohms). As the bridge only consists of resistors, we can expect a very broadband device. However, this is not always the case; if we observe the circuit closely, we can see that the detector port is not ground referenced, i.e any detector must be able to make differential measurements to maintain the Bridge’s balance. This is obviously not what typical spectrum analysers or RF power meters can do, as there inputs are single ended ground referenced. So to make single ended measurements we must employ some kind of single ended to differential converter. The simplest approach uses a passive balun using a Transmission Line Transformer. However, if this were to be embedded in some RF instrument, we could actually just rely on the fact that most modern RF IC’s such as mixers, ADC’s have differential inputs to begin with, so we can interface them to the bridge directly using some conditioning circuitry of course.

Anyhow, as a simple test, I built one and milled the PCB in house:

DC-Balun

Two of the resistors shown previously, are not in the schematic above because they represent our DUT (on the OUT port) and some LOAD standard/reference (REF port).

This is what the board looks like after assembly:

directional-coupler.jpg

Now to characterise the directional coupler, we must compare it to an ideal directional coupler. What would an ideal directional coupler produce at the detector port when terminated into a perfect 50 Ohm load? Zero ofcourse, as it there will be no reflection present. However, this is obviously not the case with real world directional couplers, for various reasons. For our topology the biggest non-ideality is the performance of the balun: It is not a perfect single ended to differential converter and presents some phase and amplitude errors, i.e the differential outputs are not perfectly balanced. Furthermore, the the return loss on the OUT port is also far from perfect, specially due to my DIY fabrication process. What all this means is finite Directivity – a figure of merit for directional couplers. In summary, directivty represents the bogus reflection present even when the DUT is a perfect 50 Ohm, we can think of this as fundamental limit on return loss measurements that we can make. As an extreme case, imagine our DUT has a return loss of 40dB while our directivity is mere 20dB. Using the coupler in such an instance means we incorrectly measure the DUT return loss as 20dB. Generally speaking, we can only measure DUT return loss upto 5-10 dB below the bridge directivity. So the best way of thinking about directivty is simply the Dynamic Range of return loss measurements. But things get a bit worse. If such a bridge is used manually, ie reading only the magnitude of the DET port, accuracy is terrible as the return loss of your DUT approaches the Directivity of the bridge. Just because your bridge has a directivity of 30 dB doesnt mean manual measurements can measure return loss of upto 30 dB.

To understand this we have to remember that the bogus reflection that limits our directivity can combine with our actual reflection signal with a phase that varies with frequency. A scalar detector cannot discriminate the phase of the bogus reflection thus cannot null it out: the uncertainty in scalar return loss measurements is very high. The only way to improve accuracy is to make vector measurements of the DET port at each frequency. This gives us information about the amplitude and phase of the bogus signal, which can then be subtracted (vectorially ofcourse) from the actual DET signal.

The DC shown above is still under improvement. As it stands directivity is around 21dB from 100 MHz upto about 800 MHz. The main short comings are the balun, and the fact that I compare a 50 ohm terminator with 0805 resistor to determine directivity . This is not suitable for the 3GHz VNA im designing, but a step in the right direction. Keep an eye on this post for updates.

UPDATE 1:

Based upon the problems with the first one, I designed V2. This version is firstly smaller to minimise trace parasitics, the traces are thicker in an attempt to match impedances on the cheap 2 sided FR4. Finally, the balun is followed up a coaxial-in-ferrite balun to enhance CMRR. The results are a much improved balun, totally suitable for the VNA upto 1 GHz. My signal generator cannot go beyond that.

20180901_122739.jpg

dir

UPDATE 2:

To be honest I was expected better performance than that with the new bridge. Particularly worrying was the degradation in performance after 1 GHz and the peaking around 450 MHz. So I began investigating it.

20180901_151145.jpg
The old 50 Ohm standard

To measure directivity I was using a SMA-BNC adapter and a 50 Ohm BNC terminator. I dont quite remember where I got this from but I questioned how good of a 50 Ohm load reference it really was, specially for high frequencies. Perhaps the degradation and peaking is due to the variation in parasitics between the 2 terminators used as the DUT and REF. To test this theory I decided to construct my own SMA terminators using a SMA edge connectors and a single 0805 49.9 resistor. Together with SMA an through they formed my new 50 Ohm standard.

20180901_151221
The new 50 Ohm standard

The results were overwhelmingly amazing! There is no more peaking and most importantly directivity is flat >30 dB from 20 MHz to 1350 MHz! In fact at 1 GHz the directivity is 50 dB!

dir_2

So in summary, parasitics of certain cheap adaptors do not track well between one adaptor to the other leading to a misrepresentation of the couplers true capabilities. The decline in directivity in the above graph after 1.3 GHz has less to do with the coupler design and more to do with the variability between the two SMA throughs used. This is confirmed by replacing the SMA through with a handmade short SMA pig tail through. The directivity of >=30dB then extends well into 2 Ghz, where my spectrum analyser stops. Clearly, the problem is not in the balun (atleast for these sub 3 GHz frequencies) and rather the quality of SMA terminations in use.

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