Broadband disrributed impedance matching

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But a generally useful fundamental concept.

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Bifilar winding with twisted pairs is winding with a transmission line. If you exploit the transmission line behaviour it can help, but in a lot of ap plications it's irrelevant.

Trifilar windings can also be handy, but thinking about them as transmissio n limes is a bit harder.

If you drive the transmission line so that the currents in either side of t he transmission line are equal and opposite, this does minimise common mode electromagnetic interference, but that can be a big "if".

Bifilar windings do have relatively high capacitance between the two strand s of the twisted pair.

If you look at the inductance/capacitance numbers per unit length for twis ted pair transmission lines, this falls out automatically, and it is a hand y way of estimating stray capacitance in a bifilar-wound transformer even i f you aren't driving the twisted pair as a transmission line.

Mathematical models are handy things, but they are maps of reality. Don't g et fixated on one to the exclusion of all the others.

--
Bill Sloman, Sydney

Stub filters.

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This email has not been checked by half-arsed antivirus software

Fun -- HV pulser?

Sure: the impedance is rather high, since the coils (imagine them in free air, sans core) are a pair of helical resonators. Which have pretty high impedances (typically kohms, though being short, these will be mere hundreds of ohms -- and even then, only around a pretty high self-resonant frequency), and being side-by-side, will have pretty poor coupling.

The core obviously improves the coupling, to a rather useful degree!

So, they're shitty TLTs, but that doesn't matter. ;-)

Since the winding capacitance is so low, you'll still have reasonable bandwidth (maybe up to 100MHz?), but into a fairly high impedance, a few hundred ohms. (A frequency where core loss, or its dielectric constant, may be a significant damper!) Certainly not the low ohms you need for gate driving (which I suppose is the application here).

The disparity (impedance mismatch ratio) is also the lost bandwidth ratio, more or less. So, if they're best around 200 ohms, but you use 'em at 20 ohms, expect 10s of MHz, at best. Which, for a switching application, means gate drive risetime in the 50ns range (ballpark), and switching frequencies of a couple hundred kHz.

Which is still pretty reasonable for some applications, and if you need the isolation, hell, you get only a teensy bit of inter-winding capacitance, which can be a big win.

As with any transmission line, the low frequency mismatched equivalent is inductive (if Z < Zo) or capacitive (if Z > Zo).

So, guessing from the picture but very likely the case -- Z < Zo, and the mismatch manifests primarily as leakage inductance.

CMCs fit under the TLT model still; a typical split-bobbin style one has a characteristic impedance around 300 ohms. Inter-winding capacitance is vanishingly small, a few pF. Winding self-capacitance stinks, so the frequency response also stinks. Which figures, because the winding is not even a helical resonator, but a layered bundle. So you might not even get higher order resonances (TL modes), just the first (thus, the transformer approximates unusually well as the first-order lumped equivalent).

There's a transformer that's bifilar wound, with triple-insulated wire, that has unusually good coupling (bandwidth in the 100MHz range, Zo ~ 150 ohms), and excellent balance (CT pri and sec), and high inductance AND saturation flux. I know you're fond of ISDN or Ethernet transformers, but they don't handle power, or offer reinforced isolation. It's a rare combination, and very useful for demanding data isolation and gate drive power applications.

Ah yeah, here it is: Pulse PH9185.011NL

Tim

--
Seven Transistor Labs, LLC 
Electrical Engineering Consultation and Contract Design 
Website: http://seventransistorlabs.com

I'll link my website, when I write the article about it... :^)

The basic premise is to start with a transmission line, and go from there. A real transmission line is just like a SPICE TL, except there's actually a (common mode) connection between the two ports.

This can be represented by another TL, working against "ground". I mean -- should there be such a convenience as true ground! True enough for, say, cables routed in a cable tray. But if nothing else, the impedance of free space still provides a mechanism (if a poorly defined one).

Or, if you're interested in a low frequency equivalent only, it's an inductance.

If you wind the TL into loops, that has the effect of also winding up the "grounding" TL. With shorter paths from loop to loop, you'd have to model that with a lot more ideal TL components! But if we're content to stick with the LF eq., the inductance simply increases (mutual inductance at work).

If you stick a core in there, the inductance rises even further, and you begin to approximate a SPICE TL with a real TLT. You have two ports, practically floating freely, and either terminal, of each port, can be connected to, or grounded to, anywhere you like.

Examples,

(Note that many examples are not matched-delay (Guanella) types, and thus have limited bandwidth -- peaks and nulls above the cutoff frequency, due to interference of unmatched delays, or reflections from stubs.)

As for the impedance approximations and stuff -- any introductory book on TLs talks about impedance as a function of frequency. When mismatched, the impedance appears one way or the other, and as frequency goes up, you get peaks and valleys where the impedance reverses.

Of course, the impedance reverses periodically, for a straight, dispersion-free TL. It's aperiodic for a lot of dispersive structures, like solenoids (helical resonators), or helico-toroidal resonators (i.e., single layer progressive toroidal windings).

So, in the low frequency limit, the TL looks like a single pole, inductive or capacitive (or two poles, i.e., a bit of both. And since the equivalent is given by the TL dimensions, impedance and mismatch, the mismatch-bandwidth tradeoff appears (much as gain-bandwidth occurs with dominant-pole compensated op-amps).

So no, I don't have anything quantitative, but this should be more than enough to get you started on a proof of your own. Which, I would dare say, will be more rewarding. :^)

I also kind of don't care, because practical effects (the connection that transitions from nice smooth TL into the circuit at large; L/C strays in the circuit; and how they all interact in circuit: essentially the poorly-conditioned problem of numerically solving polynomial roots, but with an infinite number of roots necessary to represent the transmission lines!), means that, even if there's a coefficient in there (which there probably is, if you're pushing close to the cutoff frequency, and need precision) -- the fact that the hand-wave simply *works*, to within a factor of 2, say, and the fact that you're usually using this for a well-guard-banded design anyway (like the parallel impedance of a transformer being more than five times the circuit impedance), means it works out, conservatively, in your favor.

Tim

--
Seven Transistor Labs, LLC 
Electrical Engineering Consultation and Contract Design 
Website: http://seventransistorlabs.com

Except that they aren't. Which is where leakage happens. :^)

Picture:

Also talks about layers, applications, parasitics. Looks handy.

What's really interesting is when the transformer shorts out part of itself, thus preventing flux from ever leaving parts of the winding. This capacitive self-shielding effect happens in large multilayer windings.

I've measured an audio transformer (little iron-cored jobbie, some kohms primary, 8 ohm secondary) with its nominal ratio at low frequencies, _rising_ to a higher and higher ratio, at high frequencies! Because the impedance is so high, and because the winding's own self-leakage (that is, between turns, and between layers) and self-capacitance becomes dominant, effectively the inner and outermost layers do all the induction.

Indeed, under such conditions, the core really has very little at all to do with the transformer's performance. Indeed indeed, for most well-intended transformer constructions, the leakage is independent of core permeability (let that one sink in for a bit)!

Tim

--
Seven Transistor Labs, LLC 
Electrical Engineering Consultation and Contract Design 
Website: http://seventransistorlabs.com

Suppose you have a 1:1 flyback supply. So, 160VDC primary, 160VDC output. (Kind of oddball, unless you're working with toobs perhaps, but bear with me. Or, maybe that's part of the excitement? Anyway...)

Wind the transformer on a cylindrical former, like one side of a FBT "UR" core. The core choice is so that you have a long winding area, enough to need only a single layer per winding.

First layer: wind, say, 30 turns of #24. This gives a hair over 5V/turn. Let's assume there's enough core area to handle this voltage, at whatever the switching frequency is.

Wrap with tape. Make it a double layer, since we want reinforced isolation!

Second layer: wind the same number of turns, same wire, in the same direction and start and end locations.

Now, reflect upon what you've created: since the two windings start in the same location (one above the other), and follow the same path at the same pitch. You've created a twin lead transmission line! It's just coiled (edgewise), into a solenoid.

Connect the primary 'start' to the switching transistor (this is a flyback, so it'll be, maybe a 500V 6A MOSFET, or something like that). The 'finish' end connects to +VIN.

If you did the conventional thing with the secondary, you'd connect the 'start' to ground, and the 'finish' to a diode (A-K) to +VOUT.

But, if you did that, then when the transistor switches, you have to charge up the entire transmission line with Vp-p (which is twice +VIN)! That's a Metric Shitload of common mode noise!

Now sure, you might make the excuse that, if you had wound the primary and secondary in bank sections (consider

for instance: each section has a winding on it, pretty cool), you could do just as well, without all the isolation capacitance ruining everything. Perhaps.

But suppose you simply flip one winding. Obviously, you flip the diode too.

This way, when the transistor switches, the primary 'start' voltage transitions, and the secondary 'start' transitions. Ideally, zero voltage develops across the transmission line!

In fact, we can better view the transformer action now, because we're coupling the transistor to the diode, through a transmission line port (that is, the two pins of an ideal TL, which, ideally, float with respect to whatever voltage you reference the port to -- no common mode current at all). On an instantaneous basis, the TL port has a resistance of Zo, so the instant the switch turns off (say), load current transfers from primary to secondary, with a voltage drop (across the TL port) given by V = Ipk * Zo.

That voltage difference propagates down the winding, hits the far end (one which is "grounded" to +VIN, one which is "grounded" to +VOUT), reflects back (in phase if open circuit, out of phase if the end is shorted -- which will be the case if a Y1 capacitor bridges between primary and secondary grounds!), propagates back up, and appears again at the primary side.

Indeed, you could put a capacitor between the switch node and the secondary (rectifier) node, and it would look suspiciously like a coupled-inductor SEPIC!

So, on average (i.e., over a switching cycle), no common mode current is generated! There is a transient spike, which in fact, is given by the TL properties of the transformer. Which can perhaps be made very short (this transformer might only need a meter of wire, which is all of 10 nanoseconds round-trip), and thus easily shunted (with Y1 cap) and filtered (with CMC).

So, okay, it's not /free/ of common mode, but because the voltages are (ideally) matched on both primary and secondary, by magnitude and by space (where the windings start and finish, and that they are coincident), there is no coupling of the full switching edge into the output.

In this way, you can make quite low power flybacks, at high frequency and efficiency, without also busting your balls on EMI filtering. A conventional windup would be challenging, because the winding /and/ isolation capacitances need to be very small, to get the impedance high (~kohms -- consider a 320Vp-p turn-off rising edge, with Ipk under 0.1A -- it'll be slooow with much of any capacitance!). This way, the (always modestly valued, say ~100 ohms) transmission line impedance actually helps, while the winding impedance itself (which, in this example, takes the form of a ferrite-loaded helical resonator) stays nice and high.

Tim

--
Seven Transistor Labs, LLC 
Electrical Engineering Consultation and Contract Design 
Website: http://seventransistorlabs.com

Yes, but not mine. Pockels cell driver.

Lots of leakage l. So the designer applied about 100 volt drive to the primaries!

The TLT ratio is indistinguishable from zero per cent!

--

John Larkin         Highland Technology, Inc 

lunatic fringe electronics