5 questions about an Op-amp driving a 10k:10k transformer

[gregwbush]

Hi

I'm just hoping to be educated a little more on these circuits by R.G.



The main question in my mind is really is the frequency response going to be the same and why?

Thanks

[R.G.]

Other than unity gain versus a gain of 2.1, what's the difference?

In designing circuits, there is a difference between what is absolutely the minimum you can get away with and what you'd do if you could take your time and do the proper job. To a large extent, the difference in the two circuits is the degree to which I put in parts to take care of the eccentricities of the transformer.

The first one is assuming a well behaved opamp and transformer and that nothing would go wrong. The second adds some parts to allow for possible - but not absolutely certain - problems. For instance;

Why these capacitors?

The capacitors are to reliably block any DC, no matter how small, from the transformer primary. This is necessary because opamps are not perfect, and can have a DC offset that would allow the "DC" field in the transformer to creep to the edge of saturation, causing distortion. A capacitor prevents this. There are three capacitors because with a bipolar supply, the DC conditions on the caps is not reliably positive on one or the other side. So it needs a bipolar cap. 100uF bipolars are hard to find and expensive, so I made up an effective bipolar from two unipolars. The 0.1uF is to "bypass" the electros at high frequencies when their imperfections might cause high frequency loss.

Why this resistor?

Two things. It isolates the opamp output from the transformer impedance, and it prevents high currents from flowing if there are certain fault conditions with the transformer. The first is the most important to your questions. Opamps are by no means perfect devices, and they do have limits on how much current they can source and sink, especially at high frequencies. That transformer is an unknown load. Bounded, perhaps, but could be anything within the boundaries. That being attached to the output of the opamp could interact with the loss of gain of the opamp and the opamp's natural phase shifts at high frequencies to cause it to oscillate. Worse, the transformer oddities that would do this are the leakage inductance and winding capacitance, which are only very rarely specified for small, cheap transformers. That 100R resistor means that the reactive funnies can't exert as much effect on the opamp's feedback node, so it makes it much more unlikely to oscillate. Or (thing #2) be damaged if there is a fault condition from the transformer trying to shove voltage spikes back from the transformer to the opamp. The resistor keeps the current flow down to where the opamp's internal catch diodes (they don't tell you about those diodes much in casual opamp learning) can clamp the incoming current to one of the power supplies without damage. Both of these things may never happen. But they might happen sometime, and resistors and caps are cheap insurance.

Why these values?

I can't remember. Which article is this from?
In any case, that's not a frequency response issue. The bass rolloff from 2.1 down to 1.0 is set at the corner of 10K and 2.2uF, about 7.23Hz, good enough not to notice for guitar and bass.

Same frequency response?

No. This is for reasons to do with the transformer, not so much the opamp circuit, with the exception of that 100R resistor. Transformers are not nicely behaved, which is one of the reasons that they're avoided in most situations where something else will do. That transformer looks to the opamp like it is a composite of a modest inductance (the leakage inductance) in series with the parallel combination of the primary inductance, a shunt capacitance to ground, and the transformed load impedance, which is itself reactive.

There is much more to picking a transformer than selecting the voltage ratio and impedances. You can get two vastly different responses from two nominally 10K:10K transformers. The differences will lie in the usually-unspecified leakage, self-capacitance, winding resistances, and the value and nonlinearity of the primary inductance.  Getting the imperfections to be small requires both extra material in the transformer and more labor expended in careful winding. So the big issue in the differences in these circuits is first which transformer you picked.

However, at least the first circuit was intended to extend the low frequency response of the transformer to allow the use of a cheaper transformer. The low frequency rolloff of a transformer itself is dependent on the primary inductance. Primary inductance is both hard to predict and variable in operation, but to contain the complexity, we decide to approximate it by some not-too-far-off single value. Most small signal transformers only tell you the inductance indirectly, by telling you the low frequency response with a certain load. The reflected secondary load appears to the opamp to be in parallel with the primary inductance. So the opamp drives current into both the primary inductance and the reflected secondary load. When the primary inductance "eats" as much signal current as the reflected load, that's generally taken as the low frequency -6db point. Below that the primary inductance subtracts ever more of the incoming signal current from what's available, leaving less for transforming to the secondary.

But both those ideas assume that there is some source impedance driving the primary. Since the primary eating the available current is the problem, you can extend frequency response by making more current available, so the secondary still gets enough to not sag at low frequencies. That's what the first circuit does. The output impedance of a good opamp is down in the milliohms, and the LM833 in particular can hump a lot of current in and out, so it makes more current available to "hide" the increasing losses to the primary inductance.

And it's why the second circuit doesn't do this so good. The 100R limits the current and makes the source impedance seen by the transformer primary be 100R, so there is not as much current available to drive the primary. The value of that resistor can be let vary from 0 to infinity; at 0, there is a lot of low frequency extension available for driving a transformer that was cheap and had a low primary inductance.

The cheap transformers I intended for use in the first circuit were specified at a low frequency rolloff of 300hz. Driving it directly from an opamp, this dropped to a measured 60Hz  -6db point. The second circuit would not do that well. There's another several pages of how to estimate the actual effect of increasing the series resistance from 0 to 100R or beyond, but I think by now you're getting the idea.

We haven't talked about high frequency response. Transformer high frequency response is dominated by the leakage inductance and secondary loading, as well as self capacitance to some extent. Leakage inductance appears as though it's in series with the primary, and its rising impedance eats more of the signal voltage as frequency rises. The cheap, small signal transformers I was designing for had leakage low enough for the maker to specify a response from 300Hz to 3kHz, good enough for telephone voice, not good enough for music. They actually did much better. I measured a few and they all went to tens of kHz. Most actually had a hump of about 8-10db at just over 20kHz. Some of them had BIG resonant peaks. That's what the 10K + 0.001uF is: it loads the primary side with a 10K resistance and damps secondary resonances at high frequencies at the cost of loading down the signal more at frequencies above 15.9kHz. Also helps the opamp see a stable load there and not oscillate.

So - yes, frequency responses will be very much the same everywhere except at the very lowest end. The difference there is in the value of the 100R resistor, lower values being better, but also introducing some chance of problems with faults and oscillation. But generally you'd get away with it for guitar.

[PRR]

EDIT -- R.G. typed more, faster, than me. Take his words as authoritative. I'll post because maybe I've touched something he didn't.

An op-amp can output true DC.

Transformer impedance at DC is (ideally) zero.

Any stray DC out of the opamp will cause "infinite" DC current in the transformer. Both the opamp and the transformer are strained.

We can't hear, and don't want, DC in audio.

Transformer and cable impedance also goes toward zero at very high frequencies. This can disturb the opamp's internal action so it starts howling MHz instead of our precious audio.

The R and C isolate the opamp from such troubles.

100R is a good value for most audio opamps. It is not large enough to matter to our typical >2K audio loads, but when loads are tending to zero it leaves the opamp able to control its own action.

The 100R interacts with the inductance and raises the transformer's bass limit. However there is another ~~1,000 Ohms inside the transformer (winding resistance), so the effect of another 100R is very small.

The C should be ample for the load and lowest frequency. If you just pencil 10K and (say) 20Hz, you get 1uFd.

However a cap and a coil will resonate. Bass bump. Computing this effect might take me a half hour. If brain-work is worth $10/hr, this is $5 cost, and we still have to buy the cap(s). Simply over-sizing the caps shoves the resonance far below the audio band, and "over-size" for 1uFd may be only $2 worth of inexpensive e-caps.

Also, e-caps are imperfect. They add distortion before they reduce bass. It is general good practice to up-size e-caps in coupling applications 10X to 100X to significantly reduce bass distortion. Here R.G. has up-sized "1uFd" by a factor of 50, which seems ample for the purpose.

E-caps only take DC one way, the other way they turn into a short. As we don't know the polarity of any stray DC out of the opamp, we have to cover both ways. You can buy "non-polar electrolytic" which have opposing internal oxide films. These are common in loudspeaker crossovers (and in motor-starting). Not common in other audio DIY parts-piles. Two polar e-caps back to back do the same thing, with convenient parts.

I call the 0.1uFd across the e-caps a "frill". It will work fine without it. With old (1960s) e-caps, something as big as 100uFd might show rising impedance at the top of the audio band. A typical 0.1uFd will be "flat" out to a MHz. Also the 0.1uFd may be lower ESR through the audio midrange, "bypassing" the e-caps' flaws. Modern e-caps are much better, and I've never found it makes a difference. OTOH the cost is small and it satisfies audiophiles who "have heard" this is a good idea.

For _my_ own use, I would just do 100R and 22uFd polar e-cap. In my experience the stray DC here should "never" be enough to bother an e-cap, and I know I no longer hear the high-highs. If a build screw-up puts reverse voltage on the cap, I replace it. However if you put your name on it for thousands of less-experienced builders to use, better to Do It Right to minimize complaints.

Why a gain of 2.1?? I don't know.

Why ~~10K gain-set resistors? A good size for most opampery. Low values (1K) strain the opamp to drive them. High values (100K) add hiss. Lower R here means bigger C at the bottom for the same bass-limit here. In mike preamp gain-set we sometimes go as low as 5 Ohms, which suggests ~~4,700uFd cap, which is a monster even before you deal with the Polar issue. (Interestingly, non-polar caps serve well for many years.)

[gregwbush]

Wow thanks for the comprehensive replies.  That helped immensely already...

R.G. the circuit snippets basically came from http://www.geofex.com/FX_images/TransformerSplitter.pdf, just cut out the switching.  Just to clarify, and correct me if i'm wrong. That A/B/Y is intended to boost as well. And that's all that the 10k,11k,2.2uF effectively do, having nothing to do with getting more out of the cheap transformer(s), and a plain unity gain buffer would be fine for a boostless version.

Thanks again. Cheers