The G word: How to get your audio off the ground (Part 3)
[Part 1 introduces the topic of grounding and "GND-think." Part 2 considers the ideal differential input.]
This article originally appeared in Linear Audio, a book-format audio magazine published half-yearly by Jan Didden.
Impedance Balance vs. Current Balance
A confounding aspect of diff amps is that the input currents are almost never equal. Here’s the situation. If I hold one input of a 10x diff amp at ground potential and drive the other, I get a factor 11 discrepancy in the input current, depending on which is the one that gets driven (Figure 15). And so, the unsuspecting engineer might naïvely reason, the input impedance is out of balance and should be put right.
Figure 15: The Imbalance Illusion.
What they do in response to this misconception is quite ghastly (figure 16).
Figure 16: Grisly outcome of cognitive illusion.
You can easily see why there is something suspect about this. If, instead of driving the circuit with one leg grounded, we drove it with a symmetrical signal, the ratio between the input currents would no longer work out as 11:1 but as 21:1. You can’t scale the impedances in a way that the currents work out equal under all conditions.
What’s going on here? Remember to think of a differential input as forming a Wheatstone bridge along with the source resistances. If you add source resistors to the above circuit you get something that is clearly no longer a difference amplifier as shown in figure 17.
Figure 17: Why it’s grisly.
We should repair the circuit and make the two legs equal again. We once again have a fully functional diff amp in figure 18. If the input currents are different, this is no indication of imbalance.
Figure 18: Wei Wu Wei, or how balance is restored by not intervening.
We should have seen from the start that the problem was illusory. In order to contrive it we had to drag the output reference of the difference amp into the equation and falsely assume that this is the point that the common-mode input impedance refers to. The circuit is balanced, certainly, but it just so happens that the input impedance references the virtual short, not some handy point that someone calls *GND.
Take-home messages
• Converting a circuit to differential does not require additional amplification stages.
• Each signal has its own reference.
• Making a circuit differential is not the same as building two independent copies of a ground-referenced one.
• Do not try to equalise signal currents. It doesn’t work and you’ll end up creating an impedance imbalance of heroic proportions.
next: In From the Cold
In From the Cold
As a means of immunising your circuit to circulating currents in the ground plane, difference amplifiers and more generally differential circuits are a fantastic idea. As a means to building a robust interface with the outside world they need an extra ingredient.
We mentioned earlier that the sensitivity to common-mode errors depends strongly on the input impedance. The lower it is, the more crucial matching will become. After all, a low input resistance will convert any common-mode voltage into a common-mode current, and any matching error will then go on to convert that into a differential-mode voltage at the input.
Diff amps, for reasons of noise, are low-impedance affairs and hence their balance is easily upset by a source impedance imbalance. For connections to the outside world it is good practice to buffer the input signal.
The circuit we get is called the instrumentation amplifier;
Figure 19: The instrumentation amplifier.
This circuit is usually drawn with the first stage not just buffering the input, but providing all of the gain as well. There is a significant incentive to doing so. Note how, regardless of any mismatches of Rf1 and Rf2, the first stage will never convert common mode into differential mode. The common-mode component is passed through unchanged but only the differential-mode component is amplified. The ability of the second stage to tell the two apart is multiplied by the gain of the first stage. Gain in the buffer stage adds free common-mode rejection.
I can sense certain sections of the readership bristle at this point. Isn’t adding an extra amplification stage in the signal path worse than the illness? Well, if you’re of that mindset I can only say: try it. You’ll discover that modern op amps change the sound a lot less than the noise added by a single unbalanced connection.
There is a reason for the sprawling cottage industry that audiophile cables have spawned. Unbalanced connections affect the sound quite strongly for reasons that by now should be quite obvious. The whole idea of having one of the actual signal wires also do the dirty work of shunting equalising currents away is crazy. To then try and solve the problem by eliminating those currents is bone-headed. To try and mollycoddle the sonic defects this causes by making outlandish cables is madness. The RCA connector and all it stands for should be banned by law.
Where was I? Oh yes, instrumentation amps. It would be a wonderful world where we could just connect the noninverting inputs of the first pair of amps to the outside world. This is not quite practical because they tend to leak. This is why input resistors were assumed. The ones we wanted to make as large as possible to keep common-mode voltages from becoming input currents.
Let’s see. There could be two ways of looking at them. Ideally we’d want them to be low enough so that when the input gets unplugged the bias current of the op amp inputs doesn’t produce a DC shift big enough to get a thump out of the speakers. Looking at the data sheets of commonly used op amps that would still only be in the 10k-s. Or we could lessen the requirement and ask merely that the bias current doesn’t cause the input to drift off more than a few volts. After all, the source might be AC coupled.
Well, we can get both right. The signal that thumps the speaker is a differential DC component. Strapping a sufficiently small resistor (tens of kilo-ohms) across the two input terminals will fix that;
Figure 20: Optimal input biasing.
We can now afford to allow both inputs to drift off-centre by several volts if need be. It’s common mode: so what. So let this resistance be large (megohms). It’s effectively the common-mode impedance we need maximised, not the differential-mode one.
What we’ve done really is to insert a large resistor Rcd in series with the receiver side ground leg of the Wheatstone bridge of Figure 8. This resistor will greatly reduce the current flowing through the signal wires. Calculating the exact impact on CMRR is left as an exercise to the reader. Meanwhile, the two input resistors ensure that the bias currents of the two op amps do not result in a too large differential-mode DC voltage, even when one terminal is tied down and the other left floating.
The same arguably holds for the source end. If the output can be floated, this too will limit conversion of common-mode voltages into current. But while it’s trivial to achieve common-mode input impedances in the megohms range, other than using a transformer, doing the same on the source side is very daunting indeed. Unless there are pressing reasons to build an electronically floated output I shouldn’t bother.
The elephant(s) in the room here are input filters. While virtually unknown in high-end consumer audio, input filters are invariably added to properly designed kit to ensure that the music continues in the presence of mobile phones and taxi dispatches.
Input filters are expected to block RF as it tries to enter the enclosure. They comprise capacitances of 100 pF or more, directly connected to the chassis. They are an integral part of the Wheatstone bridge, are rarely matched and drive down the common-mode input impedance. 2x 100 pF at 20 kHz works out as about 40 k. That’s a long way from the megohms we can get at DC.
The problem has been quite elegantly solved by Bill Whitlock [Ref 3], who uses a boot-strapping technique to increase the common mode impedance of the input filter. Do look it up. Unfortunately the only way to use this method is to buy ICs from the current licensee of his patent.
Take-home messages
• The unbalancing effects of mismatch in the source resistance are exacerbated by low common-mode input impedances.
• A non-inverting differential gain stage allows very high CM input impedances and reduces matching requirements in the diff amp stage.
next: Wiring Up
Wiring Up
Balanced audio cables are shielded twisted pairs. You can often make a perfectly good connection with an unshielded twisted pair provided all boxes live roughly at the same potential (to keep from over-driving the common-mode voltage range of some inputs) but "often" is not good enough in the real world.
So far I’ve treated differential connections as they should be: as two wires. Confusingly, XLR connections have three pins. Pins 2 and 3 are the non-inverting ("hot") and inverting ("cold") wires. So far, so good. Pin 1 though, is designated "ground." By now we know to ask the question: what on earth is meant by such an ambiguous word?
In spite of much confusion there is a clear and unambiguous answer. It should be connected in a way which allows the shield (the braid that goes around the signal pair) to perform its function. That function is to make a tunnel-like extension between two chassis inside which the actual signal pair is well-protected (figure 21). That’s what "shield" means.
Figure 21: What the cable shield is for.
Ideally we want the shield to bond directly to the rim of a circular hole in the chassis on both ends. If this is impossible, try to get as close to this ideal as you can. To get an idea of the effectiveness of a cable shield, consider this: the current through a hollow conductor does not create a magnetic field inside that conductor. All of it is outside the shield and hence around the signal wires as well.
It’s the same neat trick that makes coax cables work. A high-frequency current through the shield induces the same voltage along the inner conductor as along the shield. At high frequencies the input voltage of a coax cable (as measured between the conductor and the shield) is the same as the output voltage. By the same token, the shield serves to reduce the common-mode voltage at the receiving end of a balanced audio cable.
Figure 22: CM reduction effected by shield.
How high is high? Well, practically speaking, for a normal braided shield and a cable of a few metres long, this effect starts becoming noticeable from a few hundred Hertz upward. Below that the shield is still a pure resistance and the full voltage differential along the shield appears as common mode.
For this to work the shield should be bonded to the chassis with the lowest possible impedance. The shield itself should be a neat cylinder round the signal pair and have low resistance too. A foil shield with a drain wire is a no-no, because the drain wire concentrates the current onto itself and defeats the common-mode reducing effect up to frequencies well above the audio band. In fact, it may even preferentially couple noise into one of the two signal wires, thereby turning shield current into a differential mode error. This effect is known as Shield Current Induced Noise (SCIN). [Ref. 4]
next: The Pin 1 Problem
The Pin 1 Problem
The XLR connector has been something of a missed chance. It should have been a round shell with just two pins in it. Nobody would have doubted that the shell should connect at the chassis. But now it’s got the third pin which has misled people into thinking that it was some kind of "audio ground" connection that should connect somewhere other than the shell.
What happened is that a lot of people connected pin 1 to their internal zero volt reference (infelicitously called GND). Instead of shunting away circulating currents into the chassis, this actually invites them in to have an all night party, romp around in the furniture and be sick all over the carpet (Figure 23).
Figure 23: The Pin 1 Problem: follow the current.
Circuits designed according to the differential method explained earlier are insensitive to pin 1 problems. The PCB copper fill functions more like a chassis than a reference.
Later in our demo project we’ll be cheerfully tying pin 1 and the shell to the ground with no ill effect. But this is not how most equipment is designed. Most are single-ended internally and they do use ground as a global reference. "Ground current" means current through your internal reference. Instead of being a handy point to bond the cable shield to chassis, pin 1 has inadvertently been turned into an input.
Pin 1 problems drive users mad. The trouble is that they affect input and output connectors equally. You can induce hum in many products by feeding current into pin 1 of an output. So you could be fooled into thinking that "there’s no hum on the output" because there’s only hum when it’s connected to a specific input. And that input gets the blame.
Oftentimes the blame is placed on "ground loops." Well DUH! That’s like blaming a broken teapot on gravity. Cases where you have no loops are so rare that they’re almost accidents. Circulating currents in audio cables are mostly unavoidable. It’s just plain good engineering practice to make equipment immune to them.
At some point the problem became so prevalent that the AES had to enshrine the obvious into a standard. Called AES48, it patiently explains that the shield should be connected to the chassis via the shortest possible route and that connections between the PCB ground and the chassis should be made elsewhere;
Figure 24: The right way to connect pin 1.
Fortunately that’s all you need to do to solve the problem. Informed studio techs don’t even bother hunting down hum. They simply open up every box right after delivery and modify it so that it is AES48 compliant. Exit hum.
You should take the exhortation to keep the connection between pin 1 and chassis short very seriously. Cables get subjected to mobile phone radiation and worse. If the connection between pin 1 and the chassis is a long piece of wire, that radiation is now inside your chassis.
Take-home messages
• The cable shield is an effective tool to reduce common-mode noise. In order to work it has to be a nice, round cylinder with the signal pair neatly in the centre, and it needs to be bonded straight to the chassis on both ends.
We’ve learned a lot. Next, we’ll put a few things in practice. In Part 4: Demo project: a balanced volume controller.
References
[3] Whitlock, Bill, A New Balanced Audio Input Circuit for Maximum Common-Mode Rejection in Real-World Environments, AES preprint 4372.
[4] Brown, Jim; Whitlock, Bill, Common-Mode to Differential-Mode Conversion in Shielded Twisted-pair Cables (Shield-Current-Induced Noise), AES preprint 5747.
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