A Clean Audio Installation Guide™

7.0 SIGNAL-TO-NOISE RATIOS

7.1  System Setup

7.2  Noise Primer

7.3  Amplification of Noise

7.4  The Electro-Voice RE-20

7.5  The Sennheiser MKH-40

7.6  An SPL Problem

7.7  The Limiting Factor

7.8  Conclusion - Setup In Practice

7.0 SIGNAL-TO-NOISE RATIOS
It is our recommendation that all audio systems be run at a maximum "nominal O VU" audio voltage amplitude of +4 dBu. As mentioned before, with ± 15 volt power supplies most op-amps will clip around +21 dBu (sine wave - RMS). This yields a headroom or overload factor of 17 dB, which we saw earlier is a bare minimum for live audio. Peak to average ratios of 16 dB have been measured on speech, and we at Benchmark have seen at least this high a ratio on percussive music. It is our design philosophy to take a 6 dB loss at the input of our equipment, thus yielding an input clip point of +26 to +27 dBu (up to +30 dBu with 20 volt supplies) and internally operating the circuits at a nominal average amplitude of -2 dBu, yielding a headroom factor of 23 dB. We then achieve the 6 dB gain makeup needed at the output stage. This allows both input and output clip points of +26 to +27 dBu and a more desirable headroom factor without much sacrifice in noise performance. The output noise floor of carefully designed equipment can reach -93 dBu or better. This yields an average signal-to-noise ratio of 97 dB and peak signal-to-noise ratio (dynamic range) of 120 dB. Many Benchmark products actually have a dynamic range of 131 dB. We recommend, therefore, that all of your equipment be capable of this high an input and output amplitude.

7.1 System Setup
It now becomes very important that you carefully set up your system. Set it so that all of the gains allow the various pieces of equipment and indeed every stage within the pieces of equipment to reach their clip points at the same time. This is done by taking the majority of the gain needed from the amplifier stage that has the lowest noise figure, the point where the system's dynamic range is established, the mic preamp. As simple as this sounds, it is the key to an outstanding system, provided the installation has been performed correctly.

7.2 Noise Primer
We at Benchmark Media manufacture microphone preamplifiers with a one dB noise figure so you may enjoy the highest signal-to-noise ratio possible. This section will include the MP-4 mic preamp, the circuit used in the MPS-400/420 microphone preamplifier systems, as an example.

Noise figure is a measure of how well an amplifier amplifies the intended signal without adding noise. In the case of the MP-4 the amplifier adds only one dB of noise to that of the original signal for amplification factors greater than 40 dB. The noise figure is referenced to the Johnson noise of the resistive portion of a transducer's source impedance.⁽¹²⁾

Johnson noise may be calculated from:

[5.0]

Where:

k = Boltzman's Constant = 1.38 x 10^-23
T = temperature of resistance in degrees Kelvin
(room temperature approx. 300° K)
R = resistance = microphone source impedance
B = bandwidth = 19,980 Hz (20 Hz - 20 kHz)

From the above formula, we see that the noise of a 150 ohm resistor at room temperature is 222.9 nanovolts or -130.82 dBu, whereas a 200 ohm resistor has a noise voltage of -129.57 dBu.

7.3 Amplification of Noise
Any amplifier, while amplifying the desired signal from a microphone, will also amplify the Johnson noise from the source resistance. Therefore, the output noise of a totally noiseless amplifier operating @ 50 dB of amplification from a source resistance of 150 ohm at room temperature would be -80.82 dBu. The MP-4's performance under these conditions is approx. -80 dBu. At its minimum amplification (18 dB), the MP-4 has an output noise floor of -94 dBu. The noise increases slowly as the amplification is increased to 40 dB where the output noise is approximately -88 dBu. From this point on, the noise will increase directly with the increase in amplification. Now that we have the tools, let's see how this understanding of noise applies to two specific microphones. Knowing the source resistance, self noise, in the case of a condenser microphone with its own amplifiers, and sensitivity, you can then evaluate the performance of any microphone with the MP-4 under various sound pressure level (SPL) conditions. In the following examples, you will notice the addition and subtraction of dB quantities that are derived from SPLs and voltages. This is possible since sound pressure level is a voltage scalar quality.

7.4 The Electro-Voice RE-20
The sensitivity of an RE-20 is 1.09 mv (-57 dBu) at 94 dB SPL input. If we use a voltage amplification of 58 dB, the output voltage of the preamp at 94 dB SPL input will be +1 dBu, and the noise of the MP-4 will be approximately -72 dBu (-130 dB EIN of the preamp +58 dB gain). If the sound pressure level is sufficient to give us an output of +4 dBu, then the average signal-to-noise ratio capability is 76 dB (+4 dBu - [-72 dBu]). The sound pressure level necessary to achieve an average output of +4 dBu is +97 dB SPL (94 dB SPL + [+4 dBu-{+1 dBu}]). The peak SPL that the system can handle is +123 dB SPL using ± 20 volt supplies, since they allow a maximum output amplitude of +30 dBu (30dBu - [+4 dBu] + 97 dB SPL). At this amplification and SPL, the preamp will reach its output clip point and yield a dynamic range of 102 dB (+30 dBu - [-72 dBu]).

7.5 The Sennheiser MKH-40
Let's examine the performance of the Benchmark MP-4 with the high output Sennheiser MKH-40-P48. This microphone has a very high sensitivity of 25 mV per Pascal (10 dynes per cm² = 1 Pascal = 94 dB SPL), and very low self noise (a condenser microphone with internal electronics) of 12 dBa. The self noise, therefore, is 1.99 µV "A" weighted. This translates to approximately -111.8 dBu. Using 18 dB of amplification at the MP-4, the combination output noise is approximately -93 dBu (20 kHz noise bandwidth). At the reference SPL of 94 dB the output of the microphone is 25 mV or -29.82 dBu. Add 18 dB of amplification and the output amplitude from the preamp. The output voltage is now -11.82 dBu @ 94 dB SPL. To get +30 dBu out (just below the clip point), the additional SPL needed is; the preamp clip point minus the output voltage at the reference SPL or:

additional SPL to be added to the reference. Adding this to the reference yields:

Thus, we have an average signal to noise ratio of 97 dB (+4 -[-93]). A peak signal to noise ratio, that is - dynamic range, of 123 dB (+30 -[-93]) at a peak acoustic input of 135.82 dB SPL. This is only possible using ± 20 volt supplies with the MP-4. This input SPL is just above the 134 dB SPL/0.5% THD point of the microphone. 109.82 dB SPL average is required at this amplification for an output of +4 dBu. Now let's apply what we have just learned to a practical problem.

7.6 An SPL Problem
If a 20-bit digital A-to-D converter (the Benchmark AD2004) has a "dynamic range" (peak signal-to-average broadband [20 kHz brick-wall] noise ratio) of 109.2 dB, an input clip point of +24 dBu into an balanced input, what is the lowest peak sound pressure level that the Sennheiser MKH-40 microphone can receive and still maintain the full dynamic range of the converter? Also, what amplification is necessary from the MPS-420 microphone preamplifier system to achieve this? The MPS-420 uses the MP-4 preamplifiers with ±18 volt power supplies.

Solution
First, since the ±18 volt supplies of the MPS-420 yield a balanced output clip point of greater than +28 dBu and the input clip point of converter is +24 dBu there will be no limitation in reaching Full Scale Digital code when driven from the MPS-420. Since the dynamic range of the converter is 109.2 dB, (Full scale digital to 20 kHz noise floor) then the converter's noise floor is:

If the microphone self noise is -111.82 dBu then the maximum amplification that we can use is
(converter noise floor - self noise), that is:

Actually, if we make both the converter and the output of the MPS-420 have the same noise voltages, they will add and we will experience a 3 dB loss in dynamic range. Hence, it is well to keep the MPS-420's output noise voltage 3 dB lower than the noise voltage of the converter (even at 3 dB lower there will be a 1.8 dB loss in range). Therefore, let's select a maximum amplification factor of:

We can round off to A = 24 dB. With 24 dB of amplification, the peak input voltage that the MPS-420 can receive is, the FSD clip point of the converter - gain of the mic preamp = peak input level from mic, which is:

From the microphone sensitivity figure given by the manufacturer, we find that @ 94 dB SPL into the mic, we have an output voltage of 25 mV = -29.82 dBu. Therefore, we can have a 29.82 dB higher SPL than the reference, where we reach the clip point of the converter. Converter input clip - sensitivity = additional SPL over sensitivity reference:

Therefore, the peak SPL (electronics clip point) is:

This converter is professional device and normally set up to take a balanced input level of +4 dBu to give a -20 dBFS on the LED meter of the converter, and +24 dBu for Full Scale Digital code. This provides 20 dB of headroom. Therefore the average SPL that we should have at the microphone is:

In this example we have worked with the commonly accepted definition of dynamic range i.e. "The difference between Full Scale Digital code and the broadband noise floor of the converter." Whereas in reality the dynamic range will extend significantly below the broadband noise floor! This is because the human hearing mechanism acts much like an FFT with averaging capability that allows us to hear below the broadband noise. We, at Benchmark, have measured and listened to tones that were at -135 dBFS, 25.8 dB below the broadband noise floor of the AD2004, (we added digital gain of 60, or more, dB after the converter). Our ability to hear below the broadband noise floor is not insignificant and we will illustrate why it is, in a moment.

Now, the above calculations do not take into account the ambient acoustic noise of our recording environment. They are meant to demonstrate how, with a given microphone, the preamp gain can be optimized to meet the common definition of dynamic range in the converter. However, this also clearly demonstrates the need, in this digital recording age, to use recording environments with extremely low ambient acoustic noise levels, if we really expect to even come close to realizing the converter's full dynamic range.

For example, If the peak SPL shown above, +123.82, is the highest that will be expected during a recording session, and the dynamic range of the converter is 109.2 dB then the converter's noise floor is at an equivalent ambient SPL of 14.62 dB plus 1.8 dB for the noise addition factor = 16.42 dB SPL. Now considering our ability to resolve signals that may be 26 dB below this broadband noise floor, we run out of positive sound pressure level given by our current definitions (0 dB SPL is 20 µPa, [microPascals] the threshold of hearing, 1 kHz - 4 kHz, in youths). And who has measured a recording venue with an ambient sound pressure level that even begins to approach 16.5 dB SPL?

If our sound source can, and normally does, produce higher peak SPLs than the 123.82 figure calculated above, we may reduce the gain of the microphone preamplifier from +24 to +18 dB (the minimum gain of the MPS-420) which will raise the SPL clip point to 129.82 dB. The average SPL will move up to 109.82. A recording venue ambient noise of +20 SPL might be able to be tolerated. Beyond a gain reduction to +18 dB, we will have to use an attenuator on the input of the preamp to get further gain reductions and this is not desirable as it will cause us to run into the self noise of the preamplifier. The next step we can take to increase the peak SPL input to the microphone is to chose the +28 dBu Full Scale Digital input setting on the AD2004. The peak clip output point of the MPS-420 operating with ±18 volt supplies exceeds +28 dBu. This buys us an additional 4 dB to approximately +134 dB SPL peak. To handle recording sessions with SPLs that are higher than this will require using microphones that have less sensitivity than the Sennheiser MKH-40 and recalculating the figures.

No matter how we try, however, we can't get away from the need for extremely quiet recording venues. Pray tell, how will we take full advantage of 24-bit converters?

7.7 The Limiting Factor
The amplification required for most microphones will typically be 40 dB or greater, and the preamplifier section will usually be the limiting factor in the output noise of a console or other electronics prior to any recording or transmission medium. Therefore, the majority of amplification needed, consistent with desired headroom, should be taken from the mic preamp, since it will have the lowest noise figure of any of the amplifying stages.

7.8 Conclusion - Setup In Practice
Proper attention to these two areas; 1) clip points made equal and; 2) maximum gain from the mic preamp; will optimize the signal-to-noise ratio of your system. Unfortunately, this author has encountered very few audio systems that were set up correctly. This, of course, results in a lowered signal-to-noise ratio (lots of noise), poor headroom (lots of distortion) and frustration (lots of it).

Go to: Sections 8.0 through 10.0