Blackmer gain cell

The Blackmer gain cell is an

The Blackmer cell, which has been manufactured since 1973, is the first precision VCA circuit that was suitable for professional audio. As early as the 1970s, production Blackmer cells achieved 110 dB control range with total harmonic distortion of no more than 0.01% and very high compliance with ideal exponential control law. The circuit was used in remote-controlled mixing consoles, signal compressors, microphone amplifiers, and dbx noise reduction systems. In the 21st century, the Blackmer cell, along with Douglas Frey's Operational Voltage Controlled Element (OVCE), remains one of two integrated VCA topologies that are still widely used in studio and stage equipment.^[1]

Development and applications

In the 1960s, American recording studios adopted

The Blackmer cell was more precise and had a greater dynamic range that prior VCA topologies but it required well-matched complementary transistors of both polarity types that could not yet be implemented in a silicon integrated circuit (IC).^[2] Contemporary junction isolation technology offered poorly performing p-n-p transistors so integrated circuit designers had to use n-p-n transistors alone.^[4] The Gilbert and Dolby circuits were easily integrated in silicon^[5][1] but the Blackmer cell had to be assembled from tediously selected, precision-matched, discrete transistors.^[2][4] To ensure isothermal operation, these metal-can transistors were firmly held together with a thermally conductive ceramic block and insulated from the environment with a steel can. The first hybrid integrated circuits of this type, the "black can" dbx202, were manufactured by Blackmer's company in 1973. Five years later, Blackmer released the improved dbx202C "gold can" hybrid IC; total harmonic distortion decreased from 0.03% to 0.01% and gain control range increased from 110 dB to 116 dB.^[6] In 1980, Blackmer released a version designed by Bob Adams, the dbx2001.^[7] Unlike earlier Blackmer cells that operated in lean class AB, the dbx2001 operated in class A. Distortion dropped to less than 0.001% but the noise and dynamic range of the dbx2001 were inferior to those of class AB circuits.^[6] This first generation of Blackmer VCAs had a very long service life; as of 2002, analogue consoles built around the original dbx202 "cans" were still being used in professional recording studios.^[8]

By 1980, complementary bipolar ICs became possible and

In the 21st century, professional Blackmer ICs are manufactured by THAT Corporation – a direct descendant of Blackmers' dbx, Inc. – using dielectric isolation technology.^[4] As of April 2020, the company offered one dual-channel and two single-channel Blackmer ICs, and four "analog engine" ICs containing Blackmer cells that are controlled by Blackmer RMS detectors.^[13]

Operation

Log-antilog principle

The Blackmer cell is a direct descendant of a two-transistor log-antilog circuit, itself a derivative of the simple current mirror. Normally, the bases of two transistors of a mirror are tied together to ensure the collector current I₂ of the output transistor T2 exactly mirrors the collector current I₁ of the input transistor T1. Additional positive or negative bias voltage V_Y applied between the bases of T1 and T2 converts the mirror into a current amplifier or attenuator^[14]. Scale factor or current gain follows the exponential Shockley formula:^[15]

${\displaystyle I_{2}=I_{1}e^{\frac {V_{Y}}{\phi _{t}}},}$^[16][5]

where ${\displaystyle \phi _{t}}$ it the

In mathematics, logarithm function is defined for positive argument only. A log-antilog circuit built with NPN transistors will only accept positive input voltage V_X or only negative V_X in the case of PNP transistors.^[19][14] This is unacceptable in audio applications, which have to handle alternating current (AC) signals.^[5] Adding direct current (DC) offset to audio signals, as was proposed by Embley in 1970,^[6] will work at a fixed gain setting but any changes in gain will modulate the output DC offset.^[5]

Four-transistor Blackmer core

The Blackmer circuit consists of two complementary log-antilog VCAs.

${\displaystyle I_{2}=I_{1}e^{\frac {V_{Y}}{\phi _{t}}}={\frac {V_{X}}{R}}e^{\frac {V_{Y}}{\phi _{t}}},}$

${\displaystyle V_{XY}=V_{X}e^{\frac {V_{Y}}{\phi _{t}}},}$ assuming equal values of R in A1 and A2[16]

At 300 K, the slope of the exponential control law equals 0.33 dB/mV (or 3.0 mV/dB) for either negative or positive values of V_X. In practice, the slope is inconveniently steep and the core is usually decoupled from real-world control voltages with an active attenuator. This attenuator, or any other source of V_Y, must have very low noise and very low output impedance, which is only attainable in op-amp-based circuits. A single-ended V_Y drive is almost as good as a symmetric balanced drive; having two V_Y terminals allows control of the cell by two independent single-ended voltages.^[4]

The gain of the Blackmer cell has an inverse relationship with temperature; the hotter the IC, the lower the slope of exponential control law. For example, V_Y=+70 mV at 300 K translates to a gain of 10 times or +20 dB. As the die temperature rises to 310 K, gain at V_Y=+70 mV decreases by 0.66 dB to +19.3 dB; at maximum operating temperature of 343 K (70 °C) it drops to +17.2 dB. In practice this shortcoming is easily overcome by using a control scale that is proportional to absolute temperature (PTAT). In dbx noise reduction systems and THAT Corp's analog engine, this is ensured by the physics of the Blackmer RMS detector, which is PTAT by design. In old mixing consoles, the same effect was achieved using positive temperature coefficient (PTC) thermistors.^[24]

Eight-transistor core

Mismatches of PNP and NPN transistors of a basic Blackmer cell are usually balanced with trimming. Alternatively, transistors can be balanced by design via inclusion of opposite-type, diode-wired transistors into each leg of the core. Each of the four legs of the modified core contains one NPN and one PNP type transistor; although they are still functionally asymmetrical, the degree of asymmetry is greatly reduced. The slope of exponential control law is exactly half of that of the four-transistor cell. This improvement was invented by recording engineer Paul Conrad Buff and manufactured since 1980 as the monolithic ECG-101 IC by Allison Research and the identical TA-101 by Valley People.^[25][26]

Eight-transistor core with log error correction

The design of a Blackmer cell IC is a compromise favoring a specific combination of distortion, noise and dynamic range of gain settings. These properties are critical for professional audio application and are interrelated and cannot be perfected simultaneously. The choice of circuit simplicity (built-in, wafer-level trimming) or lowest distortion (external in-circuit trimming) is also fixed at die level.[16]^[6]

Distortion

Distortion of a class AB Blackmer core has three main sources:

• Logarithming error due to finite parasitic resistances;
• Asymmetry of top (PNP) and bottom (NPN) transistors;
• Nonlinearity of input
  voltage-to-current converter (A1).^[20]

The first two sources are contained within the core and define distortion patterns at low frequencies. Both are suppressed by increasing transistor sizes, although effective neutralization of logarithming error is only possible in improved eight-transistor cores.[31] Large transistors have lesser parasitic resistances and are less sensitive to inevitable random area mismatches.^[31] Temporal mismatches caused by thermal gradients are avoided by careful placement of core transistors and surrounding components on the IC.^[32] The residual mismatch of PNP and NPN mirrors is compensated for with trimming, usually by injecting a very small current into one of the core's two output transistors.^[33] This creates a small, asymmetric biasing voltage of a few millivolts or less, which should ideally be proportional to absolute temperature.^[33] In monolithic ICs, this is ensured by using a thermally-coupled PTAT source of bias current.^[33] Wafer-level trimming suffers from random shifts during subsequent die packaging; wafer-trimmed ICs have maximum rated THD from 0.01% (best grade) to 0.05% (worst grade) at 1V RMS input.^[34] Further reductions to 0.001% THD require in-circuit fine trimming,^[35] which is normally performed once using a precision THD analyzer and needs no further adjustments.^[30]

The output amplifier A2 operates at fixed closed-loop gain, drives a benign constant-impedance load and does not degrade distortion.

Estimation and measurement of signal-to-noise ratio is difficult and ambiguous because of the complex, non-linear relationship between currents, voltages and noise. At zero or very small input signals, the core has a very low noise floor. At high input signals, this residual noise is swamped by far larger modulation noise containing products of shot noise, thermal noise from the core's transistors, and external noises that are injected into V_Y terminals.^[36] Higher input signals cause greater modulation: "noise follows the signal", in a nonlinear fashion.^[9]

At moderate gain or attenuation settings, noise of the core – assuming noise-free surrounding circuitry – is determined by collector current shot noise, which is proportional to the square root of emitter current.^[37] Thus lowest noise is attained in class AB cores with very small idle currents. Designs for lowest distortion require pure class A operation at the cost of higher noise. For example, in THAT Corp's ICs, increase of idle current from 20 μA (class AB) to 750 μA (class A) causes a rise in no-signal noise floor by 17 dB;^[38] in dbx, Inc. hybrid "cans" the difference was either 10 or 16 dB.^[6] In practice, there is no perfect compromise; the choice of low-noise class AB or low-distortion class A depends on application.^[39]

Noise of operational amplifiers A1 and A2 is only material at very low or very high gain settings. In class AB ICs by THAT Corporation, noise of A2 becomes dominant at gain of −30 dB or less, the noise of A2 becomes dominant at gains of +20 dB or more. At high output levels, the noise signature is dominated by noises injected via control terminals, even when proper care has been taken to suppress their sources.^[36]

Injection of noise and distortion via control terminals

Blackmer cells are particularly sensitive to interference at control terminals. Any signal arriving at V_Y port, either a useful control voltage or unwanted noise, directly modulates the output signal at a rate of 0.33 dB/mV for a four-transistor cell or 0.17 dB/mV for an eight-transistor cell. 1 mV of random noise or hum results in either 4% or 2% modulation, degrading signal-to-noise ratio to absolutely unacceptable values.^[40] Contamination of V_Y with input signal V_X causes not noise, but unacceptably high harmonic distortion.^[30]

Circuits driving V_Y terminals must be designed as thoroughly as professional-grade audio paths are. In practice, V_Y terminals are usually interfaced to external control signals with low-noise operational amplifiers directly, ensuring the lowest possible output impedance;^[30] low-cost amplifiers like the NE5532 are an inferior but acceptable alternative to quieter but more expensive models.^[41] Amplifiers of this class are characterized by audio frequency noise density of a few nV/${\displaystyle {\sqrt {}}}$Hz which, although low, will swamp other noise sources at high signal levels.^[42]

Control range

In class AB cores, off-state suppression of input signal, which marks the lowest end of control scale, reaches 110 dB at 1 kHz but deteriorates at higher audio frequencies due to parasitic capacitances. Single-in-line IC packages, otherwise obsolete, perform well in this respect due to the relatively long distance between input and output pins. Care should be taken to prevent capacitive coupling from V_X input to A1 non-inverting input.^[30] In class A cores, the control scale is inevitably narrower due to higher residual noise level.^[43]

Control voltage feedthrough

In class AB cores, at low frequencies, feedthrough of control voltage V_Y into the output signal has two principal sources: mismatches in core transistors that are reduced by increasing transistor sizes, and feedthrough of input bias current. Any DC component of V_X, and input offset voltage of amplifier A1 inject DC components into input current I₁, which are replicated at the output and modulated by the core along with the AC input signal. These sources of feedthrough can be neutralized with capacitive coupling, leaving one undesirable DC component, input bias current of A1. This current can be reduced to a few nanoamperes with bias-canceling input stages. At high frequencies, V_Y is coupled to the output node directly via collector-base capacitances of the core transistors. Differential V_Y drive does not eliminate the problem because of the different capacitances of PNP and NPN transistors.^[40] The residual V_Y feedthrough can be nulled by feedforward injection of inverted V_Y into the output node via a small-value capacitor, restoring capacitive symmetry of the core.^[40]

Class A cores, in general, are more prone to control voltage feedthrough owing to thermal gradients in the core (in class AB same gradients manifest themselves as distortion). Early class A ICs used as muting gates produced audible, low-frequency "thumps" but subsequent improvements in production ICs significantly reduced the undesirable feedthrough.^[43]

References