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Part V: Attenuation

Usually in audio signal transmission, our main concern is amplification!  Yet there are some situations that attenuation is required.  The goal is ultimately the same as amplification, which is that we want to preserve maximum possible dynamic range across different audio devices.  Amplification serves that goal by minimizing noise; whereas attenuation is normally employed to avoid distortion; however, we will see that we need to take noise into account as well.

Let’s consider attenuation at these points of signal transmission:

• microphone capsule → capsule amplifier
• microphone → microphone preamplifier
• preamplifier or other line-level output device → line-level input device
• line-level output device → microphone preamplifier
• power amplifier → speaker or headphone

Finally, we’ll consider attenuation in a passive summing network, and look at transformers as attenuators.

 

Microphone attenuation—capsule amplifier

Let’s recall the earlier article on condenser microphone design, noting that condenser microphones have an internal amplifier—most often a JFET—that is subject to being overloaded by high SPL signals.  That will be specified as the microphone’s maximum SPL handling.

Condenser microphones often have a pad switch, which may reduce the microphone’s sensitivity in a range of -10 to -20dB.  Most often, these switches act as an attenuator at the capsule, either by reducing the capsule’s polarization voltage, or alternatively, by switching a shunt capacitor into the JFET input.

The effect of either is the same:  the level of the capsule signal before the JFET is reduced, thereby increasing the maximum SPL handling of the microphone by the same amount as the attenuation.  Unfortunately, there is an undesirable effect of capsule attenuation–signal to noise ratio is reduced by the same figure, so the microphone’s self-noise specification is similarly degraded.  Thus, we ideally should only employ the microphone’s pad switch in a very high SPL environment, where the microphone’s JFET would otherwise be overloaded.

 

Microphone attenuation—microphone to preamplifier

Some microphone preamplifiers have significant minimum gain, or simply have low headroom.  One “other manufacturer” eight-channel interface device that lives in the Naiant Studio rack (and will remain unnamed) has a reasonable amount of analog headroom, but has far less digital headroom.  In any of these cases, the problem can be defined as limited dynamic range.  Our job is to fit the wider dynamic range of the microphone into that smaller box.

The technically best answer for a microphone that has not hit its unattenuated maximum SPL limit is to use an inline attenuator (or preferably the pad switch on the preamplifier, if present).  This approach can have advantages for dynamic range over using the microphone’s pad.  This is because using the microphone’s internal pad will typically result in a dB-for-dB increase in the microphone’s self-noise, whereas the noise figure (the increase in overall system noise from a circuit component) from an inline pad is often only a couple of dB.

Having recognized that, it may be that the acoustic signal level is sufficiently high (or that acoustic noise is also relatively high) that it really doesn’t make a lot of practical difference where the attenuation is employed, and if there is already a pad switch on the microphone, why not use it?  However, for a source with a very wide acoustic dynamic range, the advantage of the inline pad could be audible.

Let’s run the numbers on a hypothetical source:

Acoustic signal (peak): 124dBSPL
Acoustic noise floor: 54dBSPL-A
Microphone sensitivity: -34dBV/Pa
Microphone self-noise: 10dBA
Preamplifier EIN: -120dBA @ +20dB
Preamplifier minimum gain: 20dB
Preamplifier headroom: +20dBV

The resulting analysis:

Level at preamplifier = 124dBSPL – 94dBSPL (1Pa) -34dBV/Pa + 20dB min gain = +16dBV

Noise at preamplifier* = [54dBSPL-A – 94dBSPL (1Pa) – 34dBV/Pa = -74dBA] + [10dBA – 94dBSPL (1Pa) -34dBV/Pa = -118dBA] + [-120dBA EIN] = -74dBA

 

* noise summation is calculated as nsum = sqrt (n1 ^ 2 + …. nx ^ 2), where the noise is expressed as a voltage.  To convert between dB and voltage measurement:

V = 10 ^ (dBV / 20)
dBV = 20 * log (V)

 

In this rather typical example, there is no need for an attenuator as the peak level fits inside the preamp’s headroom at minimum gain.  Perhaps uncomfortably closely though!  If the technician desires more headroom, let’s consider the noise figure using a capsule pad vs. inline attenuator, both at -12dB:

 

Level at preamplifier = 124dBSPL – 94dBSPL (1Pa) -34dBV/Pa + 20dB min gain -12dB pad = +4dBV

Noise at preamplifier using capsule pad = [54dBSPL-A – 94dBSPL (1Pa) – 34dBV/Pa -12dB pad = -86dBA] + [22dBA (degraded by capsule pad) – 94dBSPL (1Pa) -34dBV/Pa -12dB pad = -118dBA] + [-120dBA EIN] = -86dBA

Noise at preamplifier using inline pad = [54dBSPL-A – 94dBSPL (1Pa) – 34dBV/Pa -12dB pad = -86dBA] + [10dBA – 94dBSPL (1Pa) -34dBV/Pa -12dB pad = -130dBA] + [-120dBA EIN] + [thermal noise of 1k5Ω = -126dBA – 12dB pad] = -86dBA

 

So in that case it still doesn’t make any difference where the attenuation occurs, because the overall noise is still dominated by acoustic noise.  To change that result, we’d have to assume what is probably an unrealistically low acoustic noise floor.  Let’s try 24dBSPL-A, for an incredible acoustic dynamic range of 100dB!

 

Noise at preamplifier using capsule pad = [24dBSPL-A – 94dBSPL (1Pa) – 34dBV/Pa -12dB pad = -116dBA] + [22dBA (degraded by capsule pad) – 94dBSPL (1Pa) -34dBV/Pa -12dB pad = -118dBA] + [-120dBA EIN] = -113dBA

Noise at preamplifier using inline pad = [24dBSPL-A – 94dBSPL (1Pa) – 34dBV/Pa -12dB pad = -116dBA] + [10dBA – 94dBSPL (1Pa) -34dBV/Pa -12dB pad = -130dBA] + [-120dBA EIN] + [thermal noise of 1k5Ω = -126dBA – 12dB pad] = -114dBA

 

So in that probably not very common situation, the inline pad saved only 1dB of system noise.  This analysis is a bit too biased against the inline pad, because audible noise measurements should be done using CCIR quasi-peak figures.  But since that specification generally isn’t available for preamplifiers, we use what we have!  However, if I make the microphone and preamp noise specifications 10dB worse (to match perception of acoustic noise), then the resulting (quasi-quasi peak) noise is:

Capsule pad: -105dB

Inline pad: -109dB

So the inline pad might enjoy a 4dB difference in perceived noise, in the most favorable of situations.

 

One added advantage to the inline approach is relative reduction of interference.  If the signal is attenuated at the microphone, then any interference induced into the microphone cable will be relatively larger in reference to the attenuated microphone signal.  By contrast, an inline attenuator—when correctly used at the receiving end of the microphone cable—will reduce signal and interference together, preserving signal to noise ratio.

 

Attenuators and cables

Yes, that is correct, careful reader, inline attenuators are best used at the receiving side, which here means attached to the preamplifier, not the microphone (unless an attenuating cable is used, which is properly designed with the attenuating network in the output connector).

This is not only because of interference, but also because of source impedance.  This reason has to do with the resistor ratios in the attenuating network.  Uneeda describes in great detail how attenuating networks are designed; the critical point is that only two of three criteria may be specified, with the third a calculation based upon those two:

• input (load) impedance
• output (source) impedance
• attenuation

Where the external source impedance is sufficiently low, and the external load impedance is sufficiently high, we can calculate attenuation based on the resistors used in the pad:

attenuation = 20 * log [ shunt Ω / (shunt Ω + series Ω)]

 

Let’s design a microphone-level attenuator: we’ll aim for -20dB.  With microphone pads, we want to keep the inline resistance to a minimum, to reduce the drop of phantom power voltage in the attenuator—because the microphone might need it!  The nominal microphone preamplifier load impedance is 1.5kΩ, which requires shunt resistance of 150Ω, yielding source impedance from the attenuator:

ratio = 10 ^ (-20dB / 20) = 0.1

shunt Ω = ratio * 1500Ω = 150Ω

source Z = 150Ω || (1500Ω – 150Ω + 150Ω) = 136Ω

 

Which is very close to the standard microphone source impedance of 150Ω, so that ratio works quite well.  The difficulty arises when we desire less attenuation.  Here is the calculation for -10dB:

ratio = 10 ^ (-10dB / 20) = 0.316

shunt Ω = ratio * 1500Ω = 474Ω

source Z = 474Ω || (1500Ω – 474Ω + 150Ω) = 338Ω

 

That is not horrible, some dynamic microphones are in that range.  But if for some reason we want even less, say -5dB:

ratio = 10 ^ (-5dB / 20) = 0.562

shunt Ω = ratio * 1500Ω = 843Ω

source Z = 843Ω || (1500Ω – 843Ω + 150Ω) = 412Ω

 

Where the source impedance starts to get to be a significant fraction of the following load impedance, we have the further problem of the interaction of the pad and the following amplifer.  A standard microphone preamplifier has input impedance of 1.5kΩ, but in practice values from 600Ω to 3kΩ are common.  For the last example into a 1.5kΩ load, the actual attenuation is:

20 * log [ (843Ω || 1.5kΩ ) / (843Ω || 1.5kΩ + 1.5kΩ – 843Ω)] = -6.9dB

So we need to take the load impedance of the preamplifier into consideration when designing a low-value attenuator if the value is considered to be critical.

 

The pad’s source impedance is also starting to get higher than we’d like to drive a cable, especially in a seriously difficult EMI environment, or when using very long cables (>50m) where the capacitive load of the cable starts to cause high-frequency losses:

Lowpass corner frequency (-3dB) = 1 / (2 * pi * 50m * 300pF/m * 412Ω) = 25.8kHz

Such cable effects can be eliminated by placing the attenuator at the receiving end of the cable.  This becomes even more critical as we design attenuators with higher input impedance, as with . . .

 

Line-level attenuation

Nominal line-level input impedance is 10kΩ, although it’s not uncommon for much higher values to be seen, even up to 100kΩ.  Nominal line-level source impedance is still 150Ω, although values up to 600Ω may be found, especially in consumer-level equipment.  Recall from part 1 that consumer line-level is -10dBV, which is approximately 12dB lower than the professional +4dBu standard.  Thus, attenuation may be necessary when connecting professional equipment to consumer input devices.  This may be either 12dB if the consumer device has a balanced input, or 6dB if unbalanced (because losing one leg of an active-balanced output from a professional device will drop signal level by 6dB).

Here we have a choice to make in the impedance of our attenuator.  Using the “native” difference between 10kΩ input and 150Ω output, we get:

attenuation = 20 * log (( 150Ω / (10kΩ + 150Ω)) = -36.6dB

Which is quite a bit more than we’d like!  So we have to lower the input impedance, or raise the output impedance.  Either approach may be preferred.

 

for 150Ω out:

ratio = 10 ^ (-12dB / 20) = 0.251

load Ω = 150Ω / ratio = 598Ω

 

for 10kΩ in:

ratio = 10 ^ (-12dB / 20) = 0.251

shunt Ω = ratio * 10kΩ = 2.5kΩ

source Z = 2.5kΩ || (10kΩ – 2.5kΩ + 150Ω) = 1.9kΩ

 

The first approach is probably too heavy a load for some line-level sources.  We’d like to assume that all line-level output devices can drive a 600Ω load—and many can—but there are enough on the market that cannot without increased distortion that it’s not a safe general practice.

The second approach is an easy load for the output device to drive, but has an source impedance from the attenuator that is far too high to drive a cable.  It becomes almost required to place at the receiving end of the cable.  This is the preferred approach for line-level attenuation, as the 10kΩ load can be driven by any line-level output.

Another consideration in favor of the 10kΩ attenuator is the higher operating level enabled by the lighter load due to the power dissipation in the attenuating resistor network.  Given a maximum line level of +28dBu (+26dBV), the power dissipated is:

 

VRMS = 10 ^ (+26dBV/20) = 20VRMS

Power across 600Ω = 20VRMS ^ 2 / 600Ω = 0.7W

Power across 10kΩ = 20VRMS ^ 2 / 10kΩ = 0.04W

 

Where the resistors must be small enough to fit inside of cable connectors, the power rating of the resistors is a limiting factor in the maximum input level of the attenuator.  The 10kΩ network can thus tolerate much higher input signal levels than the 600Ω version.

 

Line-level attenuation and noise analysis

Here we must consider whether attenuation is truly indicated.  Attenuation when going from professional to consumer level devices seems like a no-brainer, but is it truly?  If the professional device is operating at its nominal level, probably so.  But if the professional device has a gain control or operating level switch, why not just reduce gain?

The general principle of gain staging is to take gain at the earliest possible stage, and then maintain that level throughout the signal chain.  A traditional professional signal chain will have a low input noise preamplifier as the first device (after the microphone, of course), with sufficient gain to output +4dBu line level, and all subsequent devices (dynamics processors, equalizers, effects, mixers, etc.) will be able to operate at that level.

However, modern engineering practice often uses many non-traditional devices.  When is inline attenuation vs. gain reduction indicated?  Sometimes the technician may be uncomfortable reducing output level of a preceding device, or input gain of a following device.  What to choose? Again, the answer lies in noise analysis.

 

Let’s look at two common situations:  pro to consumer level, and pro to microphone level:

Professional device:

Max level: +20dBV

Output noise: -90dBA

Consumer device:

Max Level: +6dBV

Input noise: -100dBA

 

Pro to consumer noise, -14dB level reduction: (-90dBA || -100dBA) = -90dBA = dynamic range of 96dB

Pro to consumer noise, -14dB inline pad: (-90dBA – 14dB || -100dBA || thermal noise of 10kΩ – 14dB = -132dBA) = -99dBA = dynamic range of 107dB

 

That case seems like an obvious win for the inline attenuator, and it is if we can assume that the pro source has its full dynamic range of 110dB.  That is probably not a safe real-world assumption though!  Indeed, if the signal’s true dynamic range is only a mere 90dB, then … the inline pad makes no difference at all:

 

Pro to consumer noise, -14dB level reduction: (-90dBA +20dB -14dB || -100dBA) = -84dBA = dynamic range of 90dB (pro device output at +6dBV)

Pro to consumer noise, -14dB inline pad: (-90dBA +20dB – 14dB || -100dBA || thermal noise of 10kΩ – 14dB = -132dBA) = -84dBA = dynamic range of 90dB

 

Or, if the consumer device input is a bit noisier, say -90dBA:

 

Pro to consumer noise, -14dB level reduction: (-90dBA || -90dBA) = -87dBA = dynamic range of 93dB (pro device output at +6dBV)

Pro to consumer noise, -14dB inline pad: (-90dBA – 14dB || -90dBA || thermal noise of 10kΩ – 14dB = -132dBA) = -90dBA = dynamic range of 96dB

 

In conclusion, the inline attenuator is the technically correct answer to maximize dynamic range, but as a practical matter, it might often make little to no difference.

We get a stronger indication where the amount of required attenuation is larger:

Microphone preamplifier:

Max input level: 0dBV

EIN @ +20dB: -110dBA

Minimum gain: +20dB

 

Pro to preamp noise, -30dB level reduction: (-90dBA || -110dBA) = -90dBA = dynamic range of 80dB (pro device output at -10dBV)

Pro to preamp noise, -30dB inline pad: (-90dBA – 30dB || -110dBA || thermal noise of 300Ω shunt = -133dBA) = -110dBA = dynamic range of 100dB

 

That result holds even if the source is 20dB noisier:

Pro to preamp noise, -30dB level reduction: (-90dBA  || -110dBA) = -90dBA = dynamic range of 80dB (pro device output at -10dBV)

Pro to preamp noise, -30dB inline pad: (-90dBA +20dB – 30dB || -110dBA || thermal noise of 300Ω shunt = -133dBA) = -100dBA = dynamic range of 90dB

 

This is because we still have the acoustic noise level set below the output device’s output noise where we are using the -30dB level reduction.  The moral of this story is to use an output device’s level control to reduce the signal only until the signal’s noise floor approaches the output device’s output noise.  Beyond that, use an inline attenuator instead.

 

Power amplifier attenuation

Power amplifiers are different from line-level outputs in that they can have much higher voltage levels, as well as the ability to drive heavy loads as low as 4Ω.  The equations above are the same, just with lower values for resistance!  And the critical factor becomes the power rating of the resistors used, such that power “soak” attenuators are always rated for their maximum load as well as amount of attenuation.

Another concern in power attenuation with solid-state power amplifiers is its effect on damping factor.  Since speakers are electromechanical devices with complex impedance, the control of the amplifier over the driver is dependent upon the impedance ratio of the two.  As the output impedance of the attenuator is almost certainly higher than the amplifier (which for a power amplifier is often a small fraction of an ohm), the frequency response of the driver is affected.  This can be readily seen by looking at the impedance and frequency response curves of the driver, the latter of which is given at a nominally low driving impedance.  As the amplifier is no longer able to control the resonant peak of the driver, the effect on its frequency response becomes apparent—and quite audible!  It is thus generally best to avoid power attenuation and simply reduce the gain of the power amplifier instead.

This effect can be even worse with headphones, since the impedance curve of headphone drivers can vary significantly across the full range of the audio spectrum, and headphones are designed with input impedance anywhere between 16Ω and 600Ω.  Thus, while a 100Ω input impedance attenuator might work fine with 600Ω headphones, it is probably entirely unacceptable for a 16Ω pair.  Overall, it is best to avoid inline attenuation with headphones.

The main application where power soaks remain popular is with tube- and transformer-based guitar amplifiers, which are nonlinear devices by design.  Also, the output impedance of the power soak is often not materially different than that of the output transformer, so the particular flavor of nonlinearity is perhaps not greatly altered by the attenuator.

 

Passive summing networks

Passive summing has gotten to be a fad during this era of digital production; the belief is that resistors are somehow better at math than digital algorithms.  That is almost certainly false; resistors are mainly good at adding thermal noise, to say nothing of the noise, distortion, and jitter contribution of the required DAC / preamplifier / ADC process.  But there are also useful practical applications of passive summing networks in analog signal routing.

For a simple example, my home audio system in my TV room has more sources (four) than my very basic amplifier has inputs (one).  I could solve that with a new receiver/amplifier, or maybe even a small mixer since I don’t really need a new amp … or I could build a simple little passive summing network by placing inline resistors into cables.  I am the handy and thrifty type, so I’m going to take the approach that only costs a few dollars—the summing network!

Some theory: passive summing entails feeding multiple output nodes across inline resistance to a single input node.  There can be multiple input nodes as well, but that doesn’t matter, we will simply model them as a single input with the parallel input impedance of all of them together.

In my case, I have four output devices (let’s assume they are all 150Ω source), and my TV is 10kΩ input.  I could simply Y-cable them all together, can’t I?  Yes, and it would sound terrible!  This is because all of the output devices would see a load of:

 

load Z = 150Ω / (n-1) || 10kΩ (TV) = 49.8Ω

where n = number of output nodes, which here is four.

We also know from above that load will attenuate the signal from any given node:

network loss = 20 * log (50Ω / (50Ω + 150Ω)) = -12dB

 

That’s not the problem though; the issue is that my poor consumer output devices cannot in any way, shape, or form drive a 50Ω load without hideous distortion and extremely poor frequency response (probably they have output capacitors sized for a much lighter load, and thus will have little bass response into 50Ω).

 

I can fix those problems by adding inline resistors to my cables, effectively reducing the load to something sensible.  Let’s use 10kΩ to start:

load Z = 10kΩ (series) + (10kΩ / (n-1) || 10kΩ (TV)) = 12.5kΩ

network loss = 20 * log (2.5kΩ / (12.5kΩ)) = -14dB

That will work just fine!

 

If I was particularly concerned about noise I might use smaller resistor values.  Here I am not, because the thermal noise of a 10kΩ resistor is -118dBA, which is far lower than the noise floor of any of my output devices.  But if I were summing microphones into a single input (yes, this can be done for some applications!), I would probably use a lower value, maybe 1kΩ.  The calculations above yield the same result, but the thermal noise contribution drops to -128dBA, and there are no worries about microphones driving 1.25kΩ loads.

It is somewhat common to add a shunt resistor to a passive summing network.  This is mainly done to eliminate variation in level from different following input devices, but it’s not generally necessary from a technical perspective.

A shunt resistor will also lower the output impedance of the network (which is otherwise R / n), a helpful function if the network must be at the output end of a cable run from the input device—which I don’t generally recommend.  Here, my four-headed cable will have an output impedance of 2.5kΩ, but my total cable run is only 2m or so.  If that were a 20m run, I might want one 20m cable after the network rather than four 20m cables before, so I would use a shunt resistor (let’s use 250Ω) to reduce the network’s output impedance in front of the cable run.  Of course, that also increases the network loss:

 

network loss = 20 * log (2.5kΩ || 250Ω / (10kΩ + 2.5kΩ || 250Ω)) = -33dB

 

That is not a problem for a summing network that feeds a microphone preamplifier, but it would be a challenge for my home receiver!  So if I really needed a lower output impedance, I’d also reduce the series resistance as well.  How 3kΩ?

 

network loss = 20 * log (3kΩ / 3 || 250Ω || 10kΩ / (3kΩ + 3kΩ / 3 || 250Ω || 10kΩ)) = -24dB

 

Transformers as attenuators

Transformers are as close as we can get to a free lunch in audio signal transmission!  When we consider attenuators, we are always worried about trade-offs between noise and distortion, and maybe interference as well.

By using a step-down transformer as an attenuator, these concerns can be alleviated.  This is because of the transformer’s near-magical property (magnets, how do they work?) of reflected impedance.  That is, the output impedance of a transformer is equal to the output impedance of the preceding device, divided the square of the turns ratio between the primary and secondary.  Similarly, the input impedance is equal to that of the following device, times the square of the turns ratio.  The level drop is equal to the inverse of turns ratio.

 

For a professional to consumer line level matching transformer, we want a 4:1 turns ratio:

drop = 20 * log (1:4) = -12dB

 

If our devices are 150Ω output and 10kΩ input, the reflected impedances to our devices are 160kΩ input and 9Ω output!  Practically, the output impedance is limited by the resistance of the secondary coil, but that figure will be sufficiently low in an audio transformer as to not be of concern.  We also don’t have to worry about thermal noise, because the transformer’s relatively low DC resistance.

At the same time, the transformer can elegantly handle balanced-to-unbalanced conversion, with impressive CMRR!

Also, transformers can be reversed if we need a step-up rather than a step-down—although mind the impedances there as the same rules apply:  our 150Ω output becomes 2.4kΩ, and the 10kΩ input drops to 625Ω.  That’s a bit of a mismatch, and will thus reduce the signal gain accordingly.  A 1:3 ratio would be better here.

So if transformers are that good at everything, why not always use them?  Well … high-quality audio transformers are large and expensive.  Moderate-quality audio transformers can be of more practical size and cost, but will still be expensive compared to a handful of resistors, and might not be as linear at high level (although we often enjoy the nonlinear sound of a saturated transformer).  The resistor attenuator will usually win out on size and cost, unless a balun conversion is required.

Note that a resistor attenuator can be designed as an impedance-balancing network, when going from unbalanced to balanced, but that requires the attenuator to be placed at the unbalanced output device, possibly forcing a higher than indicated output impedance from the attenuator in front of the balanced cable.  If the cable run must be long, the transformer will be the preferred device.

 

Naiant solutions for attenuation

Naiant has the following products for attenuation solutions:

• MPD inline attenuator, in various barrel adaptor or cable configurations, for microphone, line, and instrument-level signals.  New for 2024, the MPD is available with a two-position barrel switch option.  The MPD is also available in a two or four channel summing network configuration (formerly called the MIX cable).
• VPD variable attenuator with four or eight switch positions, depending on configuration.
• ITA inline transformer adaptor for attenuation and balun applications.