Injection Transformers

Suppose you have the following situation in your development process of some linear, regulating circuitry:

  • You have designed a control loop to stabilize a physical quantity of your choice (voltage, current, resistance, power, frequency, …).
  • You have collected the characteristics of your control loop components as precise as you could, but some doubt remains because of tolerances, missing specifications and other uncertainties.
  • You have simulated the whole loop with SPICE, and everything looks stable and lethargic.
  • In reality, nothing is stable. There are oscillations, limit cycles, motorboating, …

Well, its time to measure the characteristics of your control loop instead of just guessing them, how educated ever your guess may have been. This is the moment to employ a Loop Gain Analyzer or Bode Analyzer to find out more.

These analyzers are made to plot the characteristics of closed control loops (gain and phase) by injecting a (very small) signal into the loop and to find out how the regulator reacted to it. There are commercial products that can do that (e.g. Keysights E5061B-3L5 Network and Impedance Analyzer with a frequency range up to 5Hz (!) to 3GHz, costing a whopping 35k€ list price w/o VAT), looking like this:

KeysightE5063BVnaAndImpedanceAnalyzerPicture.png

Another machinery that can do gain / phase measurements is a device called Bode 100 from Omicron Labs. This one costs a lot less (4.5k€), but is only usable up to 50MHz.

BodeAnalyzerBode100

Regardless if you do it by hand or use an expensive machine, one fundamental question always arises:

How on earth do I get my injected signal into the control loop without disturbing or altering its characteristics ? Rescue is near, here comes the injection transformer ! A good injection transformer has the following characteristics:

  • A very broad frequency range, covering the whole range of frequencies that may show up in your system. Broad frequency range means that the S21 of this transformer is really flat (0.1dB), not just 3dB down.
  • Phase stability. Over the whole frequency range of interest, allowed phase shift from input to output is only a few degrees maximum.
  • Ideally, the in-loop side of your injection transformer looks like a short circuit. What comes close is a very small resistor (max. 10-20 Ohms) in parallel with a transformer coil.
  • A good injection transformer has perfect galvanic isolation in the Multi-Gigaohms, and a very small capacitance between primary and secondary.
  • If the injection transformer lies in a signal path also running DC current, this must not saturate the transformer or change its characteristics. This primarily affects low frequencies, obviously.
  • The transformer must operate linearly in the whole range of signal amplitudes we want to inject (10mVpp should be enough).

To illustrate the use on an injection transformer, lets invent a very simple voltage regulator and insert our injection transformer there (*):

InjectionTransformerTestCircuit1.png

and now lets plot the response. We would want it to be below the input, of course, plus we want a nice gain and phase margin so nothing comes even close to oscillations.

InjectionTransformerTestCircuit1Results

Looks fine. At low frequencies, a positive input leads to a damped, negative output. There is a peak at 20kHz, but 6dB down from the input level. 60% phase margin occurs at 20dB down amplitude, so OK.

Even if its still safe, but why the peak ? Lets model some ESR into the output cap and see what happens then. Circuit now looks like this (note the ESR in the output cap):

InjectionTransformerTestCircuit2.png

Now the gain/phase looks like that:

InjectionTransformerTestCircuit2Results.png

Peak gone ! Very nice. I bet you have already heard that the ESR of output caps are the only reason why LDO regulators are stable at all.

At a last try with this simple example, lets add a speed-up sensing cap for the TL431s sense input, in series with a resistor to protect the input agains steep voltage steps (e.g., caused by a short):

InjectionTransformerTestCircuit3.png

And now the gain / phase plot:

InjectionTransformerTestCircuit3Results.png

The good life. Attenuation is 29dB now, phase is even better (look at the changed maximum frequency now, ist 1MHz instead of 100kHz).

Now, how can we create an injection transformer with all our desired characteristics as stated above ? Its probably not as easy as it looks, but lets try to formulate some specs:

  • 100Hz to several 100kHz with a phase shift below 5 degrees.
  • amplitude flatness of less than 0.2dB over this range
  • not more than ca. 20 Ohms resistance at the injected side

A small market research reveals that there are 7-decade commercial transformers for a few 100€s a piece. The other extreme is some homebrew hacks using line power transformers (I found this in a Texas Instruments application note). You can find a lively discussion between these two approaches (and their protagonists) on the net.

A wideband commercial injection transformer looks like this:

PicotestInjectionTransformerPicture

This model boasts 10Hz to 45MHz bandwidth (watch out, this is not even -3dB bandwidth, “real” 0.1dB flatness is 100Hz to ca. 1MHz only). Capacitance is a quite large 150pF. Price is a few 100€.

What I also found are some creative ideas using inductive current sensing transformers, ISDN transformers and common mode chokes.
The best device I tried was a pulse engineering 200-turn:1 current transformer with 10 handmade secondary windings and a 22Ohm injection side resistor. This part had a response from 50Hz to 400kHz (5° Phase error), a flatness of 0.2dB and a DC tolerance of a few mA. Maximum distortion free signal level at the injection side would be 10mV (ample for most measurements). This transformer was driven by an resistive input divider with 2Ohms of drive impedance (.. it is a current transformer, …) . This translates into 53dB of total attenuation (transformer plus input divider), asking for 5Vpp input into 50Ohms for a 10mVpp output, no problem for most modern function generators or AFGs. Coupling capacitance was 15pF.

Before we proceed to practical measurements, lets memorize some important constraints that must be met for meaningful gain / phase measurements:

  • the loop must be stable BEFORE any measurements can be taken. Injecting signals into an already unstable (oscillating) control loop delivers nonsense.
  • the injected signals must be small enough so that the control loops response to the injected signal is a LINEAR function of the stimulus. Driving systems into saturation can trigger all sorts of exotic nonlinear reactions (limit cycles, parametric oscillations, motorboating, creation of harmonics and/or subharmonics or other mixer products, …). Bode plots make no sense for nonlinear systems, making
    usable measurements of the stability of the system impossible.
  • The injection mechanism must not significantly alter the characteristics of the control loop itself; In other words the injection mechanism itself introduces only very small amplitude and phase errors over the frequency band of interest. This constraint can be challenging at the extreme low and high frequency corners, e.g. due to transformer limitations.
  • The system to be tested must not change its regulation characteristics (gain/phase) within the range of the injected signal (e.g. switch from constant voltage to constant current mode).
  • Stability can change depending on the load under which the system is running; Testing unloaded systems (e.g. power supply with no load) normally results in different stability measurements that systems with realistic loading (because, e.g. the output cap of a power supply and the load resistor form a time-constant that changes with the load resistor, leading to changes in gain and phase margins).
  • in order to get meaningful frequency characteristics, the injected signal needs to be strictly sinusoidal, otherwise harmonics will distort the output amplitude (and phase) measurements. This could be a challange to an injection transformer at very low frequencies, due to core saturation.
  • if the injected signal is swept over frequency, care must be taken so that the injection signal amplitude does not change via the sweeping and that any filter settling times on the analyzer side are short enough so that they do not introduce amplitude errors.
  • if an injection transformer is used, care must be taken that DC current flowing thru it does not drive the core into saturation or, at least, reduce its inductance (and thereby the low frequency limit). Usually, high-quality industrial injection transformers have limit in the range of 10mA DC.
  • if you you use an industrial injection transfomer bear in mind that they might have a hefty 100eds of picofarads as coupling capacitance. Not all circuits like that.

There are two ways to obtain points on the gain/phase curve:

  • Sweeping using a VCO controlled by a ramp generator, also driving the X axis of a scope. A detector measures the amplitude and phase and displays it on the Y axis. Curve done !
    Pros: Simplicity. No programming. Cons: Limited precision, VCO amplitude settling time, limited sweep speed, more effort for log display needed.
  • Stepping using an arbitrary function generator and a digital scope, measuring amplitude and phase.
    Pros: Accuracy, frequency range, signal quality (no spurs), elegant postprocessing of results. Cons: Some programming is needed.

Finding a Good Injection Transformer

Apart from commercial offerings, finding an injection transformer is not so easy because for the vast majority of other transformers the important specs are not published. Trial and error is left here, so (after reading some hints on the web) I tried three categories of transformers:

  • Line and Signal Transformers
  • Current Transformers
  • Common-Mode Chokes

With no simulation data available, all started with prototypes:

InjectionTransformerPrototypesSigTransformersSmall

The first samples were an ISDN signal transformer (left) and a small 0.5VA line transformer, with a termination resistor plus an attenuation network.

The ISDN signal transformer was quite usable, the line transformer had a frequency range too small to be useful.

Next, I tried current transformers with a hand-added secondary winding of 10 turns.

InjectionTransformerPrototypesCurrTransformersSmall

There were two versions with different numbers of secondary turns, PE-51687 and PE-51688. Again, a matching network was used to flatten out the frequency response. These worked quite well, and I used them in the boxed versions.

Last not least I measured some common mode chokes.

InjectionTransformerPrototypesCMChokesSmall

Due to lacking frequency response, these were considered a failure.

So, what remains are the ISDN signal transformer and the current transformers from pulse engineering.

A PCB was built for those, an example is shown below:

InjectionTransformerOnPCBPhotoSmall.png

And finally the PCBs were boxed:

InjectionTransformersBoxedSmall

Measurement Results for the boxed versions were (for the ISDN transformer):

InjectionTransformerISDNMeasurements

… and for the current transformer from Pulse Engineering (PE) …

InjectionTransformerCurrTransMeasurements

Both are usable, the ISDN signal transformer is more PCB friendly, I would say.

Datasheets of the transformers used can be found below:

Click here to see the ISDN Transformer Datasheet …

Click here for the Pulse Engineering Transformer Datasheets …

A PCB with all types of BNC mounts and for current and ISDN transformers is shown below:

InjectionTransformerPCBPicture

 

Commercial and Homemade Injection Transformers

There is a sort of Youtube battle between different manufacturers of injection transformers; some (Dr. Ridley) stress their high-power ultra-low frequency models, others  (Picotest) brag with their extremely large frequency range,  all compare apples and oranges, as usual if you desparately want to sell something. Just some facts to sober down to realistic expectations:

There is not *one* ideal injection transformer. It is always a compromise between lower and upper frequency limit, saturation current, capacitances, size and cost.

If the transformer core is small (and/or low μ), you get

  • a bad low frequency limit
  • a small saturation current (low amplitudes only)
  • low coupling capacitances and a good high frequency limit.
  • a compact and light unit

If the core is large (and/or high μ), you get

  • a good low frequency limit
  • a large saturation current
  • high coupling capacitances and a bad high frequency limit.
  • a large and heavy unit.

The first commercial injection transformer I measured was the Omicron B-WIT100. Omicron sells this as  a 1Hz to 10MHz transformer (they call this the “usable” range, that is a lot worse than 3dB). It looks like this:

BodeBWit100PictureOutside

… and inside it looks like this:BodeBWit100PictureInside.png

All the magic is a high-μ core with about 40 bifilar turns, a BNC socket, a fuse (in shrink-wrap tubing) and some 4mm sockets. The wiring is not particularly HF-like, but what do you want for a 10MHz frequency limit. The core (ca. 42mm diameter, 21mm in height) sits on some antistatic packaging material and is glued down. The only remarkable thing about this is the ca. 500€ price tag.

When measuring this in gain/phase mode on the Bode100 (input from 50Ohms, high impedance secondary) we get the following curves:

Bode100BWit100TransformerGainPhase1dB10Hz10MHz

I chose frequency limits where gain is 1dB down from the maximum, and phase error  5 degrees or less. This is my personal choice to make comparisons between various transformers. “Useful” frequency ranges cannot be meaningfully compared. OK, here we come from ca. 44Hz to 4.7MHz (-1dB) and from 243Hz to 568kHz with less than 5% phase error. Vastly different from 1Hz to 10MHz, but still not bad.

Just to be on the safe side, I repeated the measurement on the Keysight E5061B. Here it looks like this:

E5061B3L5BWit100TransformerGainPhase1dB10Hz10MHzS21

Here we have a (-1dB) range from 45.8Hz to 4.43MHz and a (+/-5°) phase range of 271Hz to 747kHz, which is in good agreement with the Bode100 results. The measurements on the Keysight were made using -20dBm of VNA power, 10Hz IF Bandwidth using the VNA (and not the LF ports) with 50Ohms, coaxial cables and a “Thru” calibration.

Dave Jones of the EEVBlog was so impressed that he thought (not serious) that these transformers were made by “Austrian nude virgins”. I was sceptical about this, and I tried to clone this using a Vacuumschmelze VAC T60006-L2030-W514 core and the same twisted-pair winding scheme. My prototype looked not as fancy as the production part from Omicron, and it has a somewhat smaller core diameter, like here:

Bode100VACT60006-L2030-WS14TransformerPictureInside.PNG

To my surprise, this part performed not bad at all, as can be seen here:

Bode100VACT60006-L2030-WS14TransformerGainPhase1dB10Hz10MHz

… and the phase limits are here:

Bode100VACT60006-L2030-WS14TransformerGainPhase5Deg10Hz10MHz

OK, here we come from ca. 111Hz to 8.6MHz (-1dB) and from 641Hz to 862kHz with less than 5% phase error. We could say that the frequency range has shifted upwards by a factor of  roughly 2. Passband attenuation is a little bit less than the Omicron model. Now the same on the Keysight E5061B-3L5:

E5061B3L5VACT60006-L2030-WS14TransformerGainPhase1dB10Hz10MHz

Here we have 118Hz to 8.05MHz for -1dB gain and 702Hz to 1.35MHz for +/-5° phase. The higher frequency limit for the phase could be the difference between a 50Ohm and a high-impedance termination on the transmission port.

In my opinion it is safe to say that the performance of the Omicron B-WIT100 can be matched by homebrew transformers provided they use a large enough high-μ core. The cost of the core I used was about 25€.

 

New Try

I could not rest until I was sure that the Omicron B-WIT100 performance could be almost exactly met by a homebrew design. So, as a bought two of the cores above, I repeated the experiment with a stack of 2 cores instead of just one and retried. I have 25 turns of bifilar wire on them now, like this:

Bode100_2xVACT60006-L2030-W514TransformerPictureInside

Total cost is now about 50€. The result surprised me:

E5061B3L5VACT60006-L2030-W514bvsBodeB-WIT100TransformerGainPhase5Hz10MHz.PNG

The fat lines are the homebrew injection transformer, the thin lines are the Omicron B-WIT100. This is almost a perfect copy, with the Omicron being 1dB better at the very low end (5Hz) and mine about 1dB better at the high end (10MHz). Measurement conditions were all on the 50Ohm S-Parameter ports via BNC cables, a full 2-port calibration, a start RBW of 10Hz and 0dBm of port power. All calibration was done using a homebrew 10MHz BNC calibration kit. The measurements look even better when you see the tolerance margins VAC has in their datasheets for their cores (a range of 1:2 !).

The next step is to find a nice Hammond box and put it there. I’ll put insulated 4mm sockets on the output side. Instead of glue as in the B-WIT100 I wanted to fix the cores in the case using a holder. I made one in a 3D printer, looking like this:

InjectionTransformerHolderSTLPicture

The cores fit in the center, and the two piles left and right provide standoffs for glass fuse holders. The STL file is free for noncommercial purposes:

Click here for an STL file of the Holder …

In my model, both primary and secondary sides are fused, and the fuses are exchangeable without soldering. The final assembly looked like this:

Bode100_2xVACT60006-L2030-W514TransformerPictureInsideBox1

I repeated the comparative measurement with the Omicron B-WIT100, giving this:

E5061B3L5VACT60006-L2030-W514bvsBodeB-WIT100TransformerGainPhase5Hz10MHzBoxed

Did not change much from the open version. At 20Hz we are half a dB down from the B-WIT100, and at the upper frequency limit the units are almost equal (fat curve the homebrew, thin curve is the B-WIT100). I am very happy with this one. EEVBlog member RX8Pilot suggested the name of NVT-1 (for nude virgin transformer), so here is the final piece:

Bode100_2xVACT60006-L2030-W514TransformerPictureOutsideBox3

Update:

I just got another commerical injection transformer for a test, the “Ridley Universal Injector” from Ridley Engineering. It looks like this:

RidleyUniversalInjectorPicture

Its a rather heavy unit (the Inventor, Dr. Ridley, weighs transformers to determine if they are any good, **), probably intended for very low frequency work. Lower range is quite low (0.1Hz), and upper range is quite high. As with other vendors, there is no specified fall off dB value, nor the termination conditions under which the values were obtained. Anyway, here is the transmission curve, with 50Ohms at the input and output, with 0dBm of drive power, from 1Hz to 50MHz, measured on a Bode100 LF VNA:

RidleyUniversalInjector100mHz30MHzS21S11at0dBm.PNG

The transmission is fairly flat until a few kHz, then there is a dip at 4.4kHz followed by a peak at 200kHz and an erratic curve until 50MHz. The extremes are more than 8dB apart. I would say, this transformer is usable very well up to ca. 3kHz, but not beyond because peaks can cause an overdrive of the control loop to be measured. The 100mHz cannot be measured here, but are plausible from the leftmost point of the curve.

No lets try this on Ridley Instruments own Analyzer, the FRA300. This one goes down to 100mHz:

RidleyUniversalInjector100mHz30MHzWithAPAnalyzer

Well, it looks very consistent above 1Hz, and at 100mHz the drop is less than 3dB. The peaks are still there, as expected. Conclusion: This is a good low-end injector working fine up to a few kHz. Why they tried to make this a 30MHz device with such an unfavourable peaking I dont know. Two transformers (one VLF, one up to some MHz, but both with a flat response) would have done a much better job, IMHO.

 

 


(*) In more complex circuitry, it is not always as obvious as here where to insert your injection transformer. With the TL431, the sense input draws no significant current so there will be no shift in output voltage due to injection transformer resistance. When the output voltage is sampled via an low-impedance divider network, things are not so simple. There are control loops where there is no accessible node to attach your injection transformer – just think of a classic LM7805 regulator. Here you need to measure output impedance by injecting current and then measuring output voltage.

(**) the rationale behind this is that you need a lot of iron and copper to keep the transformer out of saturation at very low frequencies. Motto: a transformer that a single person can lift from the floor is probably too light. This has penalties at higher frequencies, of course.