Condenser microphone pre-amp with bootstrapped op amp

Summary

In spite of allegations that op amps should not be used in audio equipment, I will show you that an OPA134 is very practicable for building a condenser/electret microphone. A bootstrapped op amp follower turns out to be an excellent device to match electrets: they only meet a discreet resistor of 1 GΩ || 2 pF, so that distortion at the higher frequencies is no item. If the design shape of this resistor has been chosen carefully, the dynamic range and the sound is to such an extent that only an ADC with a very low jitter clock will entirely show the excellent quality.
The choice for the OPA134 stems from earlier investigations.

Preface

Designing linear audio circuits you should be aware of junctions which are not biased proparly. I mean, junctions which are close to pinch off, represent a non-linear capacitance which value could double within hundred millivolts. For instance the gate capacitance of the - in HF applications very popular - JFET: J310, measured 6 pF at Ugs = -5 V, 9 pF at Ugs = 0 V and 32 pF at Ugs = 0.6 V, which is close to pinch off. So the region around 0 volt should be avoided, certainly in high impedance environments because the audio signals will phase-modulate each other.
An electret with a built-in JFET is a classic example of how it not shoud be done: the capacitance of the cartridge is in the order of 20 pF and if a bias-resistor is present, it will be at least 100 MΩ. Without this biasing-resistor Ugs will be somewhere between 0 and 0.7 V because the JFET will be biased by the leakage of the gate junction. So the capacitance is varying 1 - 10 pF with 0.1 V input.

(I leave alone the widely differing un-linear low drain-source impedance with this biasing method. Also here is a lot to say....)
In my opinion Scott Wurcer commits a terrible sin with his article [Wurcer]. In spite of sayings that op amps should not be used in HiFi applications, I will try to show you that op amps are often prefered above discrete component solutions, certainly in condensermicrophone applitations!
Of course there is a lot of dead wood but with each op amp the design has been reviewed several times so it must be better than my diy-designs. Subjects like Common Mode Rejection (CMR), Power Supply Rejection (PSR) you will get for nothing for no other reason then the equivalence of parameters on a chip. There are many types of op amps so that you could find one for nearly every application, but, why does one type 'sound' better than the other? Good question. We will come to it.

The microphone

In former days, before the electret had been invented in the late sixties, dynamic microphones had been used in low-priced applications. The electret microphone, with its built-in FET amp, was cheap and had been produced in very small cartridges which enlarged the application field. Moreover the quality of electrets became better than that of dynamic microphones, at least for not to critical applications as public address.
With the advent of the back-electret, the quality enhanced to that of the conventional expensive condenser-microphone! However, the built-in FET had not been replaced by the special tube implemented

in the condenser microphone so that recordings of e.g. live concerts remained behind.
Together with the back-electret, the quality of solid state devices became better and better so, with the right design, back-elecrtet microphones are able to compete conventional condenser microphones. That is what we are talking about here!

A condenser microphone or an electret microphone acts as a voltage source with an output impedance of - say - 20 pF. (I do not want to dig more deeply.) Such sources must be connected to amps with an input impedance in the order of 1 to 5 GΩ. The output impedance of the amp should be in the order of 100Ω. In other words we have to build an 'impedance transformer' or current amplifier.
The input impedance should be as high as possible. Therefore there is no discussion about the input device: a small, well-biased FET! But why trying to hack a discrete FET with its idiosyncrasies if there are FET op amps with high linear input impedances which promise to make much less noise than a resistor of 1 GΩ? E.g an OPA134 rustles as a resistor of 2 kΩ..... so noise is no item any more!
Using a FET-input op amp, the 'input bias current' should be < 100 pA worst case if R1 is 1GΩ.
To make 'a long story short', the unity gain stable OPA134 is a very good choice, see figure 1. The output offset will become some millivolts. If this borders you, connection 1 and 8 serve 'offset trim'.
But, what about the non-linear gate capacitance of the (well-biased) input FET? I come to this subject extensively, I promise!

The line driver

It should not be wise to use the circuit in figure 1 as a line driver as well, so we add another op amp as a buffer 'to the outside world' (figure 2). If desired, the output could be fixed to line level, why not? All the way long from the microphone to the recorder will introduce noises and hum which will be worse with low level signals. R18 and R19 are chosen equal to enlarge the common mode rejection.
The circuit in Figure 2 works well and sounds already much better than with a built-in FET. But we go for the best quality!

By the way: C2 should be a polypropylene type or a large electrolytic capacitor [Self].

Distortion

Apart from the choice of the op amp, the input impedance still borders me! The capacitances between drain and gate and between gate and source of the (small) well-biased input-FETs are in the order of 5 pF or more! Even the capacitances of these well-biased junctions change with the amplitude of the input signal, the more

because the microphone output signal is at both input connections with total different impedances and therefore could introduce a kind of common mode distortion. For these problems is a perfect solution: bootstrapping!

The bootstrap

If the power supply voltages (U₄₀ and U₇₀) of A1 should follow the output signal (U₆₀) and thus the inputs (U₂₀ and U₃₀), all dynamic capacitances are eliminated. Also partly inside the op amp circuit because the substrate has been connected to the negative power terminal. Let us see how it works: A3 repeats the output signal U_{60 of A1} to U_{10 of A3} up till 72 kHz. The pole R3 - C3 serves the stability of the loop. The six green LED's serve as two low noise zeners which are connected between two low noise current sources BC368 and BC369 (small Rbb') with a red LED at their base. For a noise arm functioning, LED's should operate at ~2 mA. The voltage across three green LED's becomes about 6 volt. The little bit of noise left, will be suppressed by C4 - R16 and C5 - R15 which form low pass poles well below the high pass poles C2 - R2 and the capacitance of the mike with R1.
A4 and A5 serve as impedance transformers so that at audio frequencies:

U_{70 of A1} = U_{70 of A5} = U_{50 of A5} = U_{10 of A3} + 6 = U_{60 of A1} + 6 = U_{20 of A1} + 6 = U_{30 of A1} + 6

Also:

U_{40 of A1} = U_{10 of A3} - 6 = U_{20 of A1} - 6 = U - 6 = U_{30 of A1} - 6

The op amp's

In the data sheet of the OPA134 I find:
Input cascode circuitry provides excellent common-mode rejection and maintains low input bias current over its wide input voltage range, minimizing distortion. OPA134 series op amps are unity-gain stable and... etc.
and,
"... TRUE FET-INPUT: I = 5pA"
and,
The distortion produced by OPA134 series op amps is below the measurement limit of all known commercially available equipment.

I stick to Burr Browns OPA(2)134 because it sounds so good in high impedance applications! Is there no better sounding one? Hardly. Henk ten Pierick developed a measuring program with which he is able to rank the sound of all kind of amplifiers (with tubes, discrete

transistors or IC's). He inputs two signals to the DUT: a rather large signal at a low frequency (say 100 Hz) and a smaller high frequency signal (at about 5 kHz) and measures the 'jitter' on the high frequncy signal at the output of the DUT. I do not go into details of his method because:
1. For his method a >$50,000 WaveCrest DTS-2075 time measurement instrument is needed so it has less sense to publish the method.
2. The human sense of hearing seems to be very susceptible to the 'jitter' low frequency signals bring about high frequency signals. You should believe this because no medical reason can be found and the IPO did not investigate it!
3. Henk does not want publishing.

Henk measured a great number of op amps...... Anyhow, an OPA134 follower scores high.

Noise performance

Circuit noise is determined by the thermal noise of external resistors and op amp noise. Op amp noise is described by two parameters: noise voltage and noise current. The total noise is quantified by the equation:

U_noise = SQRT{ (i_nR_s)² + e_n² + 4kTR_s }

With a low source impedance, the current noise term is insignificant and the voltage noise dominates the noise performance. At high source impedance, the current noise term becomes the dominant contributor. The OPA134 is unique in providing very low voltage noise and very low current noise. This provides optimum noise performance over a wide range of sources, including reactive source impedances. Refer to the typical curve: 'Voltage Noise vs Source Resistance' in the data sheet: Above 10 kΩ source resistance, the op

amp contributes little additional noise: the voltage and current terms in the total noise equation become insignificant and the source resistance term dominates. The voltage noise only dominates over the resistor noise below 2kΩ.
Condenser mikes work with very high impedances. With the OPA134, input impedances over 10 kOhm drown out the noise of the op amp, so that the choice of R1 depicts the noise performance! With assistance of Guido (TentLabs) some investigation on Internet brought us to Farnell. There was the 1 GΩ resistor:

HVF2512T1007FE: thin film chip resistor

(see the label in Photo-1). I glued it on top of the OPA134 (Photo-2). This seemed to be a good choice! I never had so little noise as with this resistor.

The microphone cartridges

The used microphone cartridges stem from the Sennheiser ME62 for the omnidirectional microphone (see Photo-3) and from the Audio-technica PRO 37R for the unidirectional one (Photo-4). With both cartridges it is rather simple to get rid of the built-in FET. With the Sennheiser the FET is simply soldered on the small PCB at the backside and with the PRO 37R the FET is located within the 'container'

on the PCB at its bottom. The cartridge can easily be separated from this container.
The capacitance of the Sennheiser is much less than that of the PRO 37R (I measured respectively 18 and 28 pF). The Sennheiser gives a 10 dB larger output signal at 1 kHz.
A TSB-165A cardioide cartridge does not have a FET at all!

Housing and cables

With my approach, the microphone needs plus and minus 12 volt from the power supply. I do not like many cables, so that the microphones are connected to a die cast box on the stand. From this box, one cable goes down to the disc recorder. The system is semi- balanced: all connections are screened, the 'return ground' as well. The return ground and the screening are interconnected only at the entrance of the disk recorder. I realise that this approach is no standard anyhow, but I did not want any compromise here!
The prototype (Photo-5&7) has been built in a rather large aluminium

die cast box. Only A1 is in the mike tube which is connected to the box with a 5-polar XLR connector. With this prototype the gain of the buffer A2 can be chosen between 24,3 and 34 dB (respectively for the Sennheiser and the PRO 37R) with a switch. During recordings I never have to correct the input signal level (it just enters the modified ADC in my home brew disk recorder).
Photo-6 shows the final result of the omni's. The small die cast box does not contain electronics anymore.

Dynamic range, noise floor

SPL measurements are not always simple. With my 'R&S ELT 2 Präzision-Schallpegelmesser' (from Marten Dijkstra) I measured the level at which my disk-recorder shows 0 dB with the microphones in question. As a 1 kHz auditory source I use a 10 cm loudspeaker in a small box. I have found:
0 dB on the recorder with the ME62's (with 24,3 dB gain) corresponds to 109 dB_SPL.
0 dB on the recorder with the PRO 37R's (with 34 dB gain) corresponds to 108 dB_SPL.
If the ME62-cartridge is replaced with an 18 pF condenser, the level meter of the disk-recorder drops down to -75 dB on the fast display and to -86 dB on the slow display. Earlier measurements (with the ME62's) showed a very small difference between an 18 pF capacitor

and a cartridge buried in a bucket with sand, hung with a rubber, in the middle of a windless night, in a separate room, so with some cautious I could conclude that the noise floor of the mike (ME62) corresponds with a sound level of 34 dB_SPL (fast) respectively 23 dB_SPL (slow)! Not bad, but these simply assembled figures stretch the truth. The noise figures are much, much better!! (see below). If we forget about the 50 Hz hum, the noise corresponds with a few dB_SPL, which verges on the incredible.

Because of its larger capacitance, the noise floor of the PRO 37R with 34 dB gain is about the same (within 2 dB) as that of the Sennheiser with 24.3 dB gain.

Measurements

Using the spectrum analyser of Adobe Audition with 16 bits - 44.1 kHz in the home brew disk-recorder with the RME DIGI96/8 PRO sound card from Intelligent Audio Solutions controlled by the rutgerS'Clock (jitter < 1 ps), we get a different image of the noise floor, but before looking at the noise from the microphone and its first stage (A1) we look at the noise from the next stage by taking off the mike from the die cast box (see Photo-5) and shortcut 2 and 4 of the XLR-plug. This offers the picture below.

The next picture shows the noise from the mike + A1, it is to say, the cartridge has been replaced by a condensor of 18 pF. As can be seen, the noise at frequencies above 1 kHz are determined by the mike and its first stage. The noise at the low frequencies are determined by the folowing stages, including the ADC inside the computer that acts as the disk recorder!
It seems that the bar-display is very sensitive to the low frequenies as seen in the previous paragraph.
At frequencies >400 Hz the noise floor is < -102 dB, at >1 kHz < -108 dB and around 50 Hz at -75 dB. The slope of the increasing noise from 1 kHz down, looks like 1/f-noise, but on the oscilloscope it looks like a 50 Hz hum signal! My headphones conferm this. There is still some work to do.....
Nevertheless a circuit of 20 pF parallel to 1 GΩ will have this type of noise [Wurcer].

Below we see a -1 dB - 1 kHz signal. For this measurement the electret has been replaced by an 18 pF capacitor with a Walter & Golterman PSE-11 in series. Mind that the second harmonic just peeks to -90 dB and the noise floor rises to -98 dB, (because of the syntesizer in the PSE-11).
These measurements have been executed with the bootstrap in action. If the bootstrap is switched off (junction of R22, C3 and + input [3] of A3 short circuited to ground) the signal attenuates 3 dB !! and the second harmonic peeks to -72 dB (not shown here).

Let us try to 'imitate' Henks measurement: add two signals via 9 pF capacitors to the input of A1 and see if sidebands will arise around the high frequency, showing Phase Modulation. There is a correlation between jitter and PM.
Below we see the result with the bootstrap in action. The 500 Hz signal (from a Philips GM2315) is about -1 dB and the 6 kHz signal (from a Philips GM2308) peeks just over -18 dB. (Mind the low noise floor of the oldies!)
Together they reach -0.5 dB. Only the harmonics of the two generators accompany the signals.

After switching off the bootstrap we get the picture below. Indeed, two sidebands arise 500 Hz from the 6 kHz only 68 dB below signal level, but I wonder if this is phase modulation. I think of intermodulation.
The special intermodulation-test on the W&G SPM-11/PSE-11 (two signals 200 Hz apart and measure at 200 Hz with an 8 or 40 Hz wide filter) on the other hand, shows an intermodulation distance of >90 dB, so......
Whatever it is, the bootstrap prevents this distortion completely.

Dynamic performance

With CLIO a number of bursts have been generated and connected to 10 Ω in series with 18 pF which replaced the microphone cartridge. Below are the plots of the recordings with 100 Hz and 4.5 kHz.

Input impedance

The data sheet of the OPA134 shows: differential input impedance = 10¹³ Ω || 2 pF.
With a 26 mV signal from the PSE-11 in series with 18 pF, the output of A1 is 23.5 mV with the bootstrap in action and 18 mV (-2.8 dB) without bootstrapping.
Ignoring the resistors in the input circuit because of their small influence (at least at 10 kHz), the calculated input capacitance becomes 1.9 pF with bootstrapping and 6.0 pF without it.

Input level

With the omnidirectional ME62 (gain 24.3 dB) the signal level of the cartridge is 155 mV for 0 dB on the display of the recorder.

Used measurement equipment

Home-brew disc recorder, running Windows XP Professional SP3, with RME DIGI96/8 PRO sound card from Intelligent Audio Solutions controlled by the rutgerS'Clock (jitter << 1 ps),

The spectrum analyser of Adobe Audition (release 1.5) with 16 bits - 44.1 kHz.

Signal generator/receiver Wandel & Goltermann SPM-11/PSE-11, 15 Hz - 200 kHz tracking oscillator (B = 8/40Hz).

Signal generator Philips GM2315, 20 Hz - 20 kHz.

Signal generator GM2308 (the 'Blokfluit'), 0 Hz - 16 kHz.

Philips AC millivolt meter PM 2451, 1 mV - 30 V full scale up to 7 MHz.

Rhode & Schwartz Präzisions-Schallpegelmesser ELT 2 - 21.7406.02

Conclusions

Building an electret microphone pre-amplifier with an op amp is simple.

The OPA134 again prooved to be a good choice.

The 1/f noise stops at 1 kHz, if any.

The dynamic range is above 1 kHz >108 dB.

The distortion of the amp and the ADC together is better than 0.001 %

The bootstrap suppresses harmonic distorsion with more than 28 dB.
The PM or second order intermodulation is prevented totally by the bootstrap.

The input impedance of the OPA134-folower enhances from 6 pF to 2 pF with the bootstrap.

The ME62-cartidge outputs 155 mV at 110 dB_SPL.

Last remarks

In the last fifteen years I have built many amplifiers for the ME62 and the PRO 37R (also see the Dutch article [PAoSU]). Electret Microfoons', on my website). The one sounded a little bit better than the other until the OPA134 with the bootstrap came in sight, together with the rutgerS'Clock in the ADC!
The progress is remarkable: strings are 'soft as butter', harps become transparent, pianos sound like live pianos, recorded concerts come into the room as re-living them, switching-off pains.

With the microphones showed above, my recordings undercut many commercial classic concert recordings.
A low jitter clock (<1 ps) is a precondition to discover the differences in full proportions.

Without the help of Henk ten Pierick I never could have made this progress!!

Some Pictures

Photo-5. The plundered PRO 37R's at the prototype-box with electronics on a stand.
Photo-6. The final result of the ME62's. The small box does not contain electronics anymore.
Photo-7. A gaze into the prototype-box.