Analogue Signal, Impedance and Grounding

Two boxes that each work perfectly will hum when you connect them. The hum is not a fault in either box. It is a fault in the space between them, and that space is what this class is about.

Levels: the ladder everything sits on#

Audio in a theatre exists at four wildly different levels, and most connection problems are a level mismatch that somebody solved with a volume knob instead of the right box.

The gap between a microphone and a line output is a factor of a thousand or more. That is why a microphone plugged into a line input is inaudible, and why a line output into a microphone input distorts horribly. Both are the same mistake in opposite directions, and both are extremely common.

Decibels, without the mysticism#

A decibel is a ratio on a logarithmic scale, and that is all. It exists because hearing is logarithmic and because multiplying gains becomes adding numbers.

• dBu is referenced to 0.775 V. Professional line level is +4 dBu, about 1.23 V.
• dBV is referenced to 1 V. Consumer line level is −10 dBV, about 0.316 V.
• dB SPL is referenced to the threshold of hearing, and is what a sound level meter reads.

Two numbers worth having permanently: 6 dB is a factor of two in voltage, and 20 dB is a factor of ten. With those you can do most level arithmetic in your head, and the decibel tool shows the working for the rest.

The trap: the difference between +4 dBu and −10 dBV is often called "12 dB", and it is actually about 11.8 dB, and the reference points are different units. When somebody says a device is "switchable between pro and consumer level", that is the switch they mean.

Impedance, and the myth of matching#

Impedance is opposition to alternating current. It is like resistance, but frequency dependent, because capacitance and inductance are involved.

Here is the thing almost everybody gets wrong, and it is worth stating flatly:

In modern audio you do not match impedances. You bridge them.

Impedance matching — making source and load equal — maximises power transfer, and it costs you half the voltage and doubles the distortion. It was necessary in the era of long telephone lines and transformers, and it survives as folklore.

Impedance bridging means making the load impedance much higher than the source, usually at least ten times. This maximises voltage transfer, which is what you actually want, because information in audio is carried by voltage.

So: a 100 Ω console output drives a 10 kΩ amplifier input. A 200 Ω microphone drives a 2 kΩ preamp input. Ratios of roughly ten to one, everywhere.

The exceptions matter. Loudspeakers genuinely are matched to amplifiers, because there you really do want power transfer. And radio frequency work, which includes the DMX and network cables in Class 9, genuinely does require matched terminations, because at those frequencies an unmatched end reflects the signal back down the cable.

Where impedance bites you#

• A guitar into a line input. Pickup source impedance is tens of kilohms and frequency dependent. A 10 kΩ line input loads it and the sound goes thin and dull. A DI box exists to present a 1 MΩ load and hand on a low-impedance balanced signal.
• Splitting one output to many inputs. Each input you add lowers the total load. Four 10 kΩ inputs in parallel is 2.5 kΩ, which is still fine from a 100 Ω source. Forty of them is 250 Ω, which is not.
• Long cable runs. Cable capacitance, roughly 100 pF per metre, forms a low-pass filter with the source impedance. From a 100 Ω source that filter is far above audio. From a 50 kΩ source over 20 m, you have lost the top end, and that is the technical explanation for why long unbalanced instrument cables sound dull.

Balanced lines: the best idea in audio#

An unbalanced connection has one signal conductor and a screen that does double duty as the return path and the shield. Any interference the cable picks up, and any voltage difference between the two boxes' grounds, adds directly to the signal.

A balanced connection sends the signal on two conductors as a difference: hot carries the signal, cold carries its inverse, and the screen carries no signal at all. At the far end, a differential receiver subtracts the two.

Now consider interference. It arrives on both conductors nearly equally, because they run together and are twisted. The receiver subtracts, the signal doubles, and the interference cancels.

That is the whole trick, and it is why every professional audio interconnect is balanced. The measure of how well it works is common-mode rejection ratio, typically 60 to 90 dB, which is a factor of a thousand to thirty thousand.

Two consequences worth internalising:

Balanced is about the receiver, not the cable. A balanced cable into an unbalanced input gets you almost nothing. The cancellation happens in the differential receiver.

The screen is not the return path. In a balanced line the screen only shields. This is precisely what allows you to disconnect it at one end to break a ground loop without losing the audio, which is the next section and the reason it works.

Ground loops, and where the hum comes from#

Here is the mechanism, and once you have it you can diagnose hum by reasoning instead of by swapping cables.

Two pieces of equipment are each connected to mains, and each has its chassis bonded to protective earth. Those two earth connections meet somewhere back at the distribution board, possibly a long way away. Because real conductors have resistance, and because other equipment is drawing current through those same conductors, the two chassis are not at exactly the same potential. A few millivolts, at 50 Hz and its harmonics.

Now you connect the two boxes with a signal cable whose screen joins the two chassis. You have made a loop: chassis A, screen, chassis B, earth conductor, back to A. A small voltage around a low resistance loop drives a current, and that current flowing through the screen's resistance appears as a voltage in series with your signal.

Fifty hertz hum. Or sixty. Plus harmonics, which is why it is a buzz rather than a pure tone, and why dimmers make it much worse: a phase-controlled dimmer chops the waveform and generates harmonics far up the audio band.

The five fixes, in order of correctness#

1. Balanced interconnects everywhere. The loop current still flows in the screen but it is not in the signal path, so it does not appear at the output. This is the real fix and everything else is a workaround.
2. Lift the screen at one end. For a balanced cable, disconnecting the screen at the receiving end breaks the loop while keeping the shielding. This is what a ground lift switch does. Label any cable you make this way, or somebody will use it as a normal cable and wonder why it is noisy in a different application.
3. A transformer, or a DI box with a lift. Galvanic isolation with no electrical path at all. The most reliable fix for a stubborn problem, and it costs some bandwidth and some money.
4. Power everything from one point. If both boxes are fed from the same distribution, the potential difference between their earths is small. This is why an audio system is fed from one source and why "the sound rack and the lighting rack on the same phase" is a real conversation.
5. Reroute the cable away from the mains run. This addresses induced interference rather than the loop, but they usually arrive together.

And the one that is not on the list:

Never disconnect the protective earth from a mains plug to cure hum.

It works. It is also how people die, and it is the single most dangerous thing done routinely in this industry. If you see a lifted earth pin or a cheater plug on a production, that is a stop-work conversation, not a note for later.

Gain structure#

Levels are not just a table to look up. Where you add the gain, along a chain of several devices, decides how much noise and how much headroom the finished signal has.

Every stage adds its own noise and has a ceiling above which it clips. The rule that falls out of those two facts:

Get the signal up to a healthy level as early as possible, then leave it alone.

Amplify at the first stage, where the noise you are amplifying is only the source's own. Amplify at the last stage and you amplify every hiss every earlier stage added, along with the signal.

The two failure modes, which sound completely different:

Gain too low early, made up later. The signal spends the chain close to the noise floor, and the final amplifier lifts noise and signal together. It sounds hissy, and turning anything down makes it worse.

Gain too high early. An early stage clips. Every later stage faithfully reproduces the distortion, and no amount of turning down afterwards removes it, because the information is gone.

Headroom is the gap between where you are running and where the stage clips: aim for around 20 dB, which feels wasteful and is what survives an actor shouting a line they have delivered quietly for three weeks.

Phantom power#

A condenser microphone needs power, and running a second cable to every microphone is unacceptable, so the power goes down the same balanced pair as the signal.

48 volts is applied through a matched pair of 6.8 kΩ resistors, to pin 2 and pin 3 equally, with pin 1 as the return. The microphone takes its supply from the difference between those pins and earth, and because both signal conductors sit at the same DC potential, a differential receiver subtracts it away and sees nothing. It is common mode, which is exactly why it is invisible to the audio.

What you actually need to know:

• Dynamic microphones do not need it and are not harmed by it, provided the cable is correctly wired. A balanced dynamic sees 48 V on both legs equally and does nothing about it.
• A miswired cable turns it dangerous. If pin 2 or pin 3 shorts to pin 1 while phantom is on, current flows through the microphone in a way it was not designed for. This is the practical reason for the pin-to-pin isolation test from Class 2.
• Never plug or unplug with phantom on. The pins make in an unpredictable order and the resulting transient goes straight into a preamp at high gain. It is loud enough to damage a loudspeaker and the people in front of it.
• Ribbon microphones can be destroyed by it, particularly older ones and particularly through a miswired cable. If you do not know what is on the end of a line, phantom stays off.
• It is not the same as T-power or plug-in power. Those are different voltages on different pins, and connecting one to the other is a repair bill.

At the bench#

Two hours and ten minutes.

Block A — Build the ladder (30 min)#

Measure the actual output voltage of: a dynamic microphone speaking normally, a phone headphone output at full volume, a console line output at 0 dB, and a small amplifier driving a speaker.

Write all four in millivolts and in dBu. Then calculate the ratio between the largest and the smallest. That number is why input stages have gain switches.

Block B — Make a ground loop, then kill it (40 min)#

Two mains-powered devices, deliberately fed from sockets on different circuits, connected unbalanced. Get the hum. Measure the AC voltage between the two chassis with everything disconnected. Record it in millivolts.

Then apply the fixes one at a time and measure the hum at the output after each: same power source, balanced interconnect, screen lifted at one end, transformer isolation. Record the improvement in dB for each.

You now have a ranked, measured list of what actually works, made by you, which is worth considerably more than the list in this document.

Block C — Impedance, demonstrated (35 min)#

Drive a 10 kΩ load from a signal generator through a 100 Ω series resistor. Measure the voltage. Now change the load to 1 kΩ, then 100 Ω, then 10 Ω. Plot voltage against load impedance.

Find the point where the load equals the source, and confirm you have lost exactly half the voltage. That is impedance matching, and the plot is the argument against it.

Then repeat with 20 m of unbalanced cable and a high source impedance, and measure the frequency response at 100 Hz, 1 kHz and 10 kHz. The top end will be down, and you can calculate by how much from the cable capacitance.

Block D — Common-mode rejection, measured (25 min)#

Inject a common-mode signal onto a balanced line, deliberately, and measure what comes out of the differential receiver. Calculate the CMRR in dB.

Then disconnect one leg of the balanced pair, so the line is effectively unbalanced, and repeat. The difference between those two numbers is why the industry standardised on XLR.

Numbers from this class#

Self test with model answers

Answer it yourself first, out loud or on paper, then open the answer. Reading the answer without attempting the question teaches you almost nothing.

1. 1Why do modern audio systems bridge impedances rather than match them?
2. 2Two working boxes hum when connected. Explain the mechanism as a circuit.
3. 3Why can you lift the screen at one end of a balanced cable but not the earth pin of a mains plug?
4. 4You hear 100 Hz rather than 50 Hz. What does that tell you and where do you look?
5. 5Why does a long unbalanced instrument cable sound dull, and what fixes it?

Note. These are model answers, not the only correct ones. If yours differs and you can defend it with the arithmetic and a measurement, that is worth more than matching the wording.