Bruce Hofer - Designing for Ultra-Low THD N in Analog Circuits

IntroductionThis presentation is a condensed, but updated version of a design track seminar I gave at the 2011 New York AES convention Everything I will talk about today is derived from my own experiences designing very high performance and state-of-the-art instruments over the past 44 years You will not find some of this material in textbooksUnfortunately I cannot disclose certain revelations for competitive reasonsOur 1-hour time constraint will also limit the number of topics A copy of todays slides can be obtained by contacting me at: [email protected]

Selected Topics for TodayTaylor Series Model of Non-LinearityEstimation of 2H & 3H distortion Resistors and CapacitorsComparison of technologiesNon-linearity models and distortion estimation Op-Amps (circa 2013)Bipolar versus JFET input stagesThe 4 major sources of op-amp distortion Some distortion reduction tricks Noise and Noise Estimation (if time)

A Non-Linearity Model that Enables Estimation of 2H and 3H DistortionUse a Taylor Series to model non-linear behavior Circuit is modeled as having a voltage dependent gain: Vout / Vs = f(Vs ) = Ao * (1 + k2* Vs + k3* Vs ^2 ) 2HD and 3HD ratios can be estimated with surprising accuracy using only 3 values for dynamic gain at the positive peak (Ap), negative peak (An) and, zero (Ao) points of an assumed sine-wave signal:2HD (k2 / 2) = |Ap An| / (8 * Ao)3HD (k3 / 4) = |Ap + An 2*Ao| / (24 * Ao) Note that 2HD (as a ratio) is proportional to Vs while 3HD is proportional to Vs^2

Example: Emitter Follower DistortionA simple emitter follower was constructed using a MPSA18 transistor with RL = 4.02k wired to -15V and the collector to +15V. Performance with a 5.0 Vpk (10.0 Vpp) signal is to be determined at +21.8C (295K) Equivalent circuit is shown on next slide The 100k load resistor represents the input impedance of the audio analyzer (dc coupled)The element Re models the dynamic impedance of the emitter-base junction Re interacts with the total load impedance to give a voltage gain that is slightly less than unity, and that varies as a function to the instantaneous signal voltage

Emitter Follower CircuitNote: Re = kT/qIe

Follower Distortion Estimation, contdDynamic emitter impedance, Re kT/qIek = Boltzmanns constant = 1.38065E-23T = 295K (ignoring self heating within the transistor)q = electron charge = 1.6022E-19 Gain is calculated at VB = -5.0, 0, and +5.0 V: VB = -5.0 V: Ie = 2.282 mA, Re = 11.138 An = 0.99713VB = 0.0 V: Ie = 3.576 mA, Re = 7.1085 Ao = 0.99816VB = +5.0 V: Ie = 4.870 mA, Re = 5.2200 Ap = 0.99865 2HD |Ap An| / 8*Ao = 0.019% (-74.4 dB) 3HD |Ap + An - 2*Ao| / 24*Ao = 0.0023% (-92.8 dB)

Actual FFT of the Follower OutputThe measured levels of 2H and 3H with a 10.0 Vpp sine-wave at 1 kHz are -75.1 dB and -93.4 dB compared to the estimates of -74.4 dB and -92.8 dB

Audio Precision is a registered trademark of Audio Precision, Inc. Copyright 2013 Audio Precision, Inc.

Resistors in Analog Design

Linear Resistor TechnologiesComposition Thick Film Thin Film or Metal Film Metal Foil Wire-Wound Some Comments about Matched Resistor Networks

Composition ResistorsThe resistive element is a compacted mixture of carbon and ceramic held together in a resin baseVery popular prior to the 1970s, much less popular todayStill useful in some non-audio applications that require high peak power capability, or super low series inductance Unimpressive performance by todays standardsTolerances from 20% to 5% TCR is typically 150 to 1000 ppm/C (worse at low values)High modulation noise and voltage coefficient compared to other types DO NOT USE in high performance analog designs!One notable exception is in the design of certain guitar amplifiers where certain forms of distortion are desired

Thick Film ResistorsThe resistive element is a conductive film applied to the surface of a cylindrical or rectangular substrateResistance is determined by film composition and etching patternVery wide variety of sizes and power ratings Very popular for general purpose applicationsTolerances of 2% to 0.1%, usually laser trimmed when

Thin Film (Metal Film) ResistorsThe resistive element is a more stable conductive film (typically Nichrome or Ta-N) that is sputtered onto the surface of a cylindrical or rectangular substrateResistance is determined by film thickness and patternLess of a variety of sizes and power ratings versus thick film types Superior performance, but much more expensiveTolerances from 1% to 0.02% (usually laser trimmed when

Metal Foil ResistorsThe resistive element is a special alloy metal foil that is cemented to an inert substrateResistance is determined by the foil characteristics and patternTrimming is accomplished by opening links in a carefully designed foil patternvastly more stable than L cut trimming The best DC performance, and most expensive of all resistor technologiesTolerances to 0.001% with TCR as low as 0.05 ppm/C !Extremely low modulation noise and thermal EMFSpecified voltage coefficient is typically

Wire-Wound (WW) ResistorsThe resistive element is wire having a low temperature coefficient and carefully wound on a substrateTypically appropriate only for lower resistance valuesVery high peak and average power ratings are possible

Winding Patterns #1 / #3 - Inductive #2 - Bifilar #4 - Ayrton-Perry

Resistor Non-LinearityResistors exhibit two general forms of non-linearityVoltage coefficient and power coefficient (thermal modulation) Resistor voltage coefficient non-linearity is best modeled as R(Vs) = Ro * (1 - kv* |Vs|)kv has units of ppm/V and is usually positiveTaylor series model is not appropriate here! Distortion can be estimated by taking the FFT of a full-wave rectified sine multiplied by the sine2HD 0, assuming no significant dc component 3HD |kv* Vs | / 5.9 Note proportionality to Vs not Vs^2 as would be expected using a Taylor series model for non-linearity5HD |kv* Vs | / 41 3HD / 7 5HD is about -17 dB below 3HD

Resistor Non-Linearity, contdResistor power coefficient non-linearity is similarly modeled as R(Ps) = Ro * (1 + kP * Ps)kP has units of ppm/W and can be either positive or negative However, the real non-linearity mechanism is thermal modulation which leads to a much more useful model: R(Vs) = Ro * (1 + TCR * Z() * (Vs^2 / Ro))TCR is the dc temperature coefficient (ppm/C)Z() is the device thermal impedance (C/W) which is a very complex function of frequencyinstantaneous power dissipation changes in a resistor do NOT cause instantaneous changes in the temperature of the resistive materialAs frequency 0, |Z()| R the dc thermal resistance, which is typically 200-300 C/W for a 1206-size surface mount resistor

Resistor Non-Linearity, contdAt very low frequencies (> R at low frequencies, thus contributing higher modulation distortion than a thin film resistor with a larger TCR

Recommendations for Audio CircuitsAll factors considered, the best resistor technology for audio applications is a low TCR thin filmAvoid the common 25 ppm/C characteristic in critical circuit locations, and pay the premium for either 10 ppm/C or 5 ppm/C Some manufacturers now offer 2 ppm/C (if you can afford it) For surface mount resistors, use only 1206 size Smaller sizes have a lower power rating hence a higher thermal resistance which translates to a higher thermal modulation distortionsizes larger than 1206 are not commonly availableLimit the signal to 20 mWpk or about 3 Vrms (+12 dBu) for the lowest distortion performanceConsider using series-parallel combinations in circuits requiring higher peak power dissipation or higher voltage

Resistor Networks Resistor networks are especially useful in applications that benefit from ratio matching Ratio accuracies can be as good as 0.01% for thin film, or an incredible 0.001% for metal foilExtremely low differential temperature coefficients at dc, however watch out for unexpectedly high thermal modulation effects with metal foil types Avoid large R ratios (e.g. 10:1 or higher)Best performance is achieved if all resistors are of equal value The small size of resistor networks (SOIC-8/-16) will mean a higher thermal impedance, thus causing higher thermal modulation distortion than discrete resistors

A True StoryAbout 13 years ago a certain manufacturer decided to change their network substrate material from ceramic to passivated silicon without notifying its customersCeramic is brittle and more expensive to process and cut to size Although the resistor DC parameters were unchanged, the AC performance was a total disaster! The stray C between each resistor and the substrate was not only higher, but NON-LINEARIt is believed that P-I-N diodes were formed between each resistor and the semi-conducting substrate, thus causing the voltage drop in one resistor to generate distortion products in the other resistorsThe manufacturer quickly added the option to specify the original ceramic substrate when told they were about to be disqualified


Capacitors in Analog Design

Linear Dielectric MaterialsPolymer FilmA generic term covering many different types of filmsExamples include polyester (PE), polyethylene naphtalate (PEN), polyphenylene-sulfide (PPS), polypropylene (PP), polystyrene (PS), and polytetrafluoroethylene (PTFE or Teflon) Ceramic Another generic term covering a very wide variety of compositions and characteristics--bewareExamples include Z5U, X7R, NP0, Hi-K Mica Glass

Polymer Film CapacitorsFilms that are widely available from many vendors:Polyester (PE), aka MylarPolyphenylene-sulfide (PPS), a relatively new film becoming more popular as an alternative to polyester with better characteristicsPolystyrene (PS), very good but has a tempco of about -100 ppm/C; can be easily damaged by soldering--film melts at +85C Polypropylene (PP), lower cost alternative to PS with very low dissipation factor and a higher melting point (+105C); but it also has a higher tempco (up to -250 ppm/C) More limited availability films:Polycarbonate (PC), very hygroscopic (moisture sensitive) must be hermetically sealed for acceptable stability, virtually obsolete todayPolytetrafluoroethylene (PTFE), aka Teflon, can be problematic due to its porosity (multiple layers are typically required for good reliability)but many audiophiles believe it just sounds better

Film Capacitor Construction Metalized FilmThe dielectric film is pre-coated with a conductive surface that is connected to one of the capacitor terminalsHas higher equivalent series resistance, hence higher dissipation factor (tan ) Metal Foil FilmThe dielectric film is interleaved with real metal foils that are connected to the capacitor terminalsLower equivalent resistance than metalized film If possible, use only foil-film construction

Ceramic CapacitorsThe only ceramic composition that should ever be used in high performance analog design is NP0 (also known as COG)Now available in values up to >100 nF with tolerances of 1-5% and voltage ratings up to 500V (1 kV for through-hole)Consider paralleling multiple caps to get higher valuesVery low dissipation factor and frequency dependence30 ppm/C specified temperature coefficient, typically 15 ppm/CExcellent stability, virtually immune to humidity

Avoid the lowest 25V rating in critical audio designs50V and 100V rated caps are not that much larger (perhaps 1206 versus 0603), but they will give superior distortion performance

Piezoelectric Effect in Some CeramicsCapacitor manufacturers are generally very secretive about their ceramic recipes (composition) Certain junk grades of ceramic capacitors exhibit a strong piezoelectric effectunwanted voltages caused by changes in physical stress within the capacitorBarium titanate (BaTiO3) is often used to increase the dielectric constant of ceramic dielectrics, thus reducing the size of a capacitor for a given C*V rating; however this substance is highly piezoelectricExamples include Z5U, Y5Y, and Hi-K Never use these lower grades of ceramic in voltage reference filters or anywhere in the audio signal path

Mica Capacitors30 years ago mica capacitors were highly regarded in the analog design communitynot so todayCommonly available with 1-5% tolerances up to about 3 nFTemperature coefficient typically 90 ppm/CGood stability, but micas brittleness can sometimes result in abrupt and unexpected value shifts with physical stress Unfortunately mica is a product of nature, some of its better sources have now been depleted With the ready availability and lower temperature coefficient of NP0 (COG) ceramic caps, there is no good reason to specify a mica capacitor anymore

Glass CapacitorsGlass is among the most stable and inert of dielectricsTypical values available up to about 2 nFExtremely stable, almost no aging, near zero voltage coefficientSome sensitivity to frequency, perhaps a bit worse than NP0 ceramics and polypropylene (PP) film capacitorsmore data welcomeTemperature coefficient is not as good as other types (typ +140 ppm/C) but glass caps can operate up to +200CHighest immunity to radiationobvious uses in military and aerospace applications (and perhaps the best choice for the survivalist golden-ears preparing for the post-apocalyptic world) Unfortunately molten glass is not so easy to form with precise dimensions5% tolerance typical, 1-2% available but hyper-expensive

Microphonic Effect in all CapacitorsIn any capacitor: d(Q) = d(C*V)The above equation if often simplified as d(Q) = C*d(V) from which the classic equation I = d/dt(Q) = C*d/dt(V) is derived However, C itself is not necessarily constantC is not only a function of voltage V (non-linearity), but it can also vary with mechanical stress/vibration thus acting as a microphoneThe total derivative is really d(Q) = d(C*V) = C*d(V) + V*d(C), thus giving I = d/dt(Q) = C*d/dt(V) + V*d/dt(C) Obvious Insight Minimize the dc potential across capacitors in series with the signal pathThe AC coupling caps in phantom powered microphone input circuits are problematic; should be as small as possible and matched in value

Non-Linearity of CapacitorsThis is a complex and proprietary subject, thus I can share only some limited comments Capacitors also have voltage coefficient effects similar to resistors, that can cause unwanted distortionInherently frequency dependent, very difficult to analyze Film capacitors, in particular, can also exhibit a non-linearity related to signal currentThe metalized surfaces or foils must be electrically connected to the external component leadsThese connections are typically physical in nature (e.g. crimped), and they often result in contact resistance (ESR) that is non-linear and variable from unit to unit


Op-Amps, circa 2013

Major Categories of Op-Amps Op-amps are ubiquitous in analog designThey are a fundamental building block enabling high performance amplification, mixing, and frequency contouring of audio signalsThey are also useful in signal analysis and generation applications Op-amps are commonly divided into four categories depending upon their intended applicationPrecision, optimized for low DC offset and bias currentGeneral purpose, usually dominant-pole compensated, but many newer designs now insert a pole-zero pair into the open loop response to get a higher GBW (gain-bandwidth product)High speed, higher slew rate, not necessarily stable under unity gain situationsReally high speed and slew rate, typically for video signals

A More Useful Classification Advances in IC processes and circuit techniques now blur these more traditional categoriesIndeed, there are a number of op-amps that feature both excellent DC performance and decent slew rate and GBW characteristics, e.g. OPA1611, OPA1641, OPA827, LT1468 (my apologies if your favorite op-amp is not in this brief list) A much more useful distinction is the input device technology: Bipolar vs. JFETBoth can offer input voltage offset performance to below 200 VHowever, JFET op-amps have near-zero input bias currentAn interesting example of a hybrid design (using both bipolar and JFET devices) is the Butler Amplifier in the dual OP275Forget about CMOS op-amps for high performance applications

Bipolar vs JFET Noise PerformanceBipolar inputs offer the lowest noise voltage rating (eN), typically 0.9 nV/Hz with the AD7970.9 nV/Hz is equivalent to the noise of a 49 resistor!But super low eN usually comes with the penalty of much higher current noise iN typically 2.0 pA/Hz for the AD797 Todays best JFET input op-amps have eN as low as 3.8-5.0 nV/Hz but iN of only 0.0008-0.003 pA/Hz!Compare the OPA827 and OPA1642 (dual) with the older bipolar models NE5534 and NE5532 (dual) Bipolar input op-amps still have a slight advantage for lower 1/f noise below 1 kHz

4 Distortion Mechanisms in Op-Amps Input stage trans-conductance non-linearityIinput = Ccomp * d/dt(Vout), [part of Ccomp may be external]Typically 3HD and proportional to F^3 in dominant pole designs Input stage common mode impedance non-linearityCaused by input capacitance variation with common mode signals, JFET input designs are much worse than bipolar Output stage or crossover non-linearityCaused by non-linear output impedance versus output current, some designs use a cancellation scheme (e.g. AD797) Mutual inductance between power supply busses and critical circuit loops

Some Distortion Reduction Tricks Output stage non-linearity can often be significantly reduced by forcing the output to behave more like a class-A amplifier by adding a resistor or a biasing dc current source to one of the supplies Watch out for increased power dissipation in the op-amp! Op-amps needing an external compensation capacitor can usually benefit from either 2-pole compensation or feed-forward compensationInstead of using the classic 22 pF between pins 5-8 of a NE5534, use a pair of 47 pF connected in series with a 499-1k resistor connected between the two capacitors and the positive supplyFor inverting NE5534 configurations, try connecting a capacitor having a value of about 6.8-12pF between the input and pin 8

Two-Pole Compensation

Feed-Forward

More Tricks to Minimize Distortion Use inverting topologies whenever possible Input capacitance is usually higher and more non-linear with common mode signals in JFET op-ampsMost op-amps will show dramatically lower THD (particularly 2HD above 5 kHz) when operated with a gain of -1 versus +1. If an op-amp must be used in a non-inverting topology (e.g. in a Sallen-Key active low-pass filter), arrange for both inputs to feel the same source impedanceThis usually means adding a complicated RC network in series with the + input to match the impedance seen looking outward from the inputTry it--the distortion reduction can be quite significant with JFET op-amps!

Common-Mode Distortion Reduction


Noise in Analog Circuits

Sources of NoiseThermal noise of resistors: VN = (4*k*T*R*BW) Shot noise of dc currents: IN = (2*q*Idc*BW) Op-Amp noise, usually eN and iN in datasheets 1/f and Popcorn noise in op-ampsMechanisms still not well understood, but under control Modulation noise in resistorsCaused by component material imperfections usually resulting in AM noise sidebands surrounding a pure tone Carbon composition is terrible, thick film is so-so, thin film is OK, metal foil and WW are best

Noise Estimation in CircuitsThe residual noise floor of many analog circuits can also be estimated with surprising accuracy using only a well designed spreadsheet! List all noise sources including resistors, op-amps, bias currentsCalculate the transfer function either from the input or output depending upon the desired resultExpress all entries in the same unit (recommend nV/Hz)Perform a root-mean-square (rms) summation of all sourcesConvert the final result to Volts by multiplying by BW where BW is the desired measurement bandwidth (e.g. 20 kHz for audio) The following slide shows an example for a prototype AP analyzer--estimates are blue, measurements are red

Range Vmin =24.047.602.400.7600.2400Range Vmax =85.326.998.532.6990.8530.270source resistance173.524173.5242.8552.8552.8552.855input dampers3743.5243.5243.5243.5243.5243.524input current limiters4423.8973.8973.8973.8976980.3950.3950.395MBUF en, ie=146 uA2.17830.91230.9123.0913.0913.0913.091MBUF in0.2531.91931.9190.3110.3110.3110.311post MBUF attenuator162152.52823.47315.2532.3472.3472.347atten Rout * in52.1723.9095.2170.3910.3910.391preamp en1.1049.37715.6154.9381.5611.5611.561preamp in1.7021.8816.9192.1880.6920.7630.241preamp Rg10002.9831.750preamp Rf40298.75531.2299.8763.1231.8440.583sum stage en2.68170.13253.80017.0135.3801.7010.538sum stage in1.6071.82222.7127.1822.2710.7180.227sum stage Ri1000184.42558.32018.4435.8321.8440.583sum stage Rf1000184.42558.32018.4435.8321.8440.583inv stage en2.6885.06626.9008.5072.6900.8510.269inv stage in1.6050.27515.8985.0281.5900.5030.159inv stage Ri140077.15124.3977.7152.4400.7720.244inv stage Rf140077.15124.3977.7152.4400.7720.244A/D driver en1.10139.52044.12013.9524.4121.3950.441A/D driver in1.7076.31124.1327.6312.4130.7630.241A/D driver Ri100092.21329.1609.2212.9160.9220.292A/D driver Rf215198.87162.88819.8876.2891.9890.629A/D 0dBFS3.961A/D noise floor-121.55765.689242.13276.56924.2137.6572.421A/D headroom3.33Tambient, C23.0measurement BW20.00924.214335.07190.91829.10912.0378.060predicted uV noise =130.047.112.794.101.6941.134measured noise =129.947.112.804.101.6971.134

Designing for Low NoiseResistor noise voltage is proportional to R Use the lowest possible resistor values that are consistent with power dissipation and distortion requirementsChoose circuit topologies that inherently minimize the value of resistors in the signal pathSeries resistor combinations may be good for lower distortion because they reduce the voltage drop across any given resistor; but they do not result in lower noise Resistor noise is proportional to T (T in K) The temperature of each resistor must be considered Use only thin-film or metal foil resistors when they must pass significant dc bias currents

In ConclusionToday we have discussed some selected topics that influence THD+N performance of analog circuits Ultra-low THD+N does not happen by accident. It is the result of careful attention to detail, clever circuit design, and the use of high quality components Some issues will continue to challenge engineers well into the future Let us not allow analog design to become a lost art


Bruce E. Hofer Chairman & Co-Founder Audio Precision, Inc.Designing for Ultra-Low THD+N in Analog Circuits

************n*******is************************

Documents

Bruce Hofer - Designing for Ultra-Low THD N in Analog Circuits