The G word: How to get your audio off the ground (Part 2)
[Part 1 introduces the topic of grounding and "GND-think."]
This article originally appeared in Linear Audio, a book-format audio magazine published half-yearly by Jan Didden.
Balance
The ideal differential input would be a transformer. By "ideal" I mean in terms of how well it would manage to look like a voltmeter with just two connections on it. Even if there were hundreds of volts between the chassis of the source and the receiver, this would go completely unnoticed. Other than that, a balanced connection will look more like Figure 7.
Figure 7. A typical transformerless balanced connection.
Vcm symbolises any voltage between the two chassis, however it arose. If the input had been a transformer, no current would flow through the two signal wires, but transformerless inputs necessarily have some input network, if only to provide a path for base currents. The task is to minimise the impact this current will have on the recovered audio signal.
Let’s assume the source is putting out 0V and redraw the circuit as a Wheatstone bridge as in Figure 8. Any signal seen between the inputs of the difference amplifier is unwanted.
Figure 8. Input/output resistances seen as a Wheatstone bridge.
It’s clear that we don’t need a transformer. We can allow current to flow through the signal wires so long as Roh/Rih = Rol/Ril. If the input resistors are well-matched and so are the output resistors, no amount of common-mode voltage will get converted into an output signal.
When a Wheatstone bridge is exactly nulled, the term we use is that the bridge is balanced. That is where the word "balanced connection" comes from. It has nothing at all to do with one voltage going up while the other goes down, but with divider ratios being equal. Don’t think uppy-downy. Think equilibrium. Zen. Ooohmmmmm…
The ratio between the error voltage and the common-mode voltage is the common-mode conversion ratio. The smaller it is, the better. It’s more common to quote this number in relation with the wanted signal, expressed in decibels. This ratio is called the Common-Mode Rejection Ratio (CMRR):
Let’s explore for a second what happens if the output resistances are matched i.e., Roh = Rol = Ro but the input resistances aren’t, say Ril = Ri and Rih = Ri + Δri:
The sensitivity to an imbalance in the input resistance increases with output resistance. It pays to minimise output resistance. It also decreases, quite rapidly, with increasing input resistance. So that seems a good idea too.
Secondly, let’s explore the impact of an imbalance in the output resistances:
This is fairly important. If your input network consists of two resistors to some local reference, making those resistors as large as you can is going to make a lot of difference. And when you measure CMRR, do so with an imbalance of several ohms on the source side because that test will tell you a lot more about the real-world ability of an input to reject CMRR than a bench test with the inputs perfectly shorted together.
next; “acting locally”…
Acting locally
The biggest overlooked opportunity for differential signalling is inside the box where small signals and large currents fight it out in cramped quarters. Think about it. Class D amplifiers switch tens of amperes in a matter of nanoseconds mere centimetres away from where the line-level signal comes in and gets processed and modulated. This is not an environment you want to try a star structure in.
Good EMI control requires a circuit board with one layer exclusively dedicated to serve as a solid copper fill or ground plane that is devoted to the one circuit node which can acceptably be called GND. This is the one that supply and signal currents return to. All decoupling capacitors are directly connected to the ground plane, as are the "GND" pins of ICs. The benefit of this relies on the fact that inside a conductor the current distributes itself inversely proportional to impedance.
When you trace all possible paths of a high-frequency current through a trace and then back to the source through a copper fill, you’ll find that the impedance is mostly inductive, determined by area encircled by that path. One path is vastly more compact than all the rest: the one where the return current through the copper fill follows every turn and twist of the trace. If you force that current around a cut in the copper fill, this spot will become strongly inductive and develop a magnetic field.
Cuts or splits in planes are an absolute no-no. Do not ever follow a chip manufacturer’s layout guidelines if they recommend using separate analogue and digital planes or making cuts in the ground plane.
At low frequencies only resistance counts. Low-frequency currents will fan out widely over all available copper. Voltage differentials will develop all over the copper fill. A "ground plane" can’t be trusted to have the same potential everywhere. A correctly designed ground plane – i.e., a contiguous one – is useless as a signal reference.
Do we worry? No. It just means we’re not going to use the ground plane as a signal reference. That should not be its function. Instead we’ll transmit every signal as a pair of wires. Now, would you believe you can do this throughout the circuit without adding active circuitry? Here’s how.
Step 1. The diff amp
In principle, you can make a differential amplifier using the classic difference amp circuit shown in Figure 9.
Figure 9: Badly drawn diff amp.
Wait. Ho. Stop. There’s something really wrong with this picture. Can you see it? Go ahead and see if you can spot it.
Here’s what. What’s the output signal in this drawing? Do we get out the magical uni-lead voltmeter again? We need to get serious about this. Every signal is two wires. Draw two: Figure 10.
Figure 10: Well-drawn diff amp.
That’s much better. We’re getting into the swing.
You see, what this circuit does is amplify the input voltage by Rf/Ri and develop that voltage between the output node of the op amp and whatever reference potential Rfl is connected to.
Figure 11 shows how it works: This provides an alternative way of looking at the difference amplifier. It is a reference translator. It’s a bit like a floating voltage source that you can reference anywhere you like.
Figure 11: Diff amp as reference translator.
But here’s the shocker: you can add reference translation ability to any circuit, if you are able to build an inverting version of it.
next: Step 2 – generalised method
Step 2. Generalised method
Suppose you have a circuit, e.g., a lowpass filter or, as the case may be, the loop filter of a class D amplifier. First, transform the circuit so that the noninverting input of the op amp is tied to the reference potential. The block called feedback network can have several inputs. In the Figure 12 example it has two: one is the signal input, the other the feedback input. It could equally have multiple signal and feedback inputs. Finally it may have a connection to the reference potential.
Figure 12: Generalised inverting circuit.
Once you’ve got that, flip the feedback network over. That’s all there is to it (Figure 13)!
Figure 13: Differential execution of inverting circuit.
The node that was originally tied to the ambiguous node called "ground" no longer needs to be connected anywhere unless required to keep the op amp input from overloading with common-mode signals. In that case the sensible place is on the ground plane near the op amp’s decoupling caps, as this is implicitly the HF reference of the op amp. Ideally the feedthrough from this point to the differential output voltage is zero, which is why we have that liberty.
We now have a proper differential pair. One wire is actively driven by the op amp, the second one is passively driven by a low-impedance tie to the ground plane that can be made pretty much anywhere. All that matters is that the whole trace has just one such connection so that the next stage, which you have also transformed in this manner, takes its input between the same pair of nodes as the feedback network.
Always route signals as two wires, one right next to the other to minimise magnetic pick-up and balance capacitive pick-up. You might need to make the passive drive connection through a zero-ohm resistor to make sure your PCB layout software understands that the second wire is to be treated as a separate net, even if it is galvanically connected, at one point, to the one called GND.
Step 3. Let the Strong Help the Weak
Some circuits don’t have a virtual-ground pendant. Circuits with potentiometers, in general, do not lend themselves well to this approach.
In that case, we can use the level-shifting capability of the surrounding circuitry to solve the problem. Imagine a problem circuit flanked by two differential circuits.
The problem circuit has a single reference node which it uses for input and output. Tie this node to the ground plane at a single point and use that for all "GND" connections of this particular subcircuit. The output of the first stage and the input of the second stage are both made to reference this point as in figure 14.
Figure 14: Extant stages as problem solvers.
I think we can see how this solves the grounding question rather magnificently. When you have a chain of signal processing stages laid out on a board with a solid ground plane, each signal run between stages is referenced at the most convenient point on the ground plane. There is no reason to try and make a global reference. The differential signal just hops from one reference to the other as it progresses through the circuit.
Part 3 will consider Impedance Balance vs. Current Balance.
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