Designing for Ultra-Low THD+N in Analog Circuits Bruce E. Hofer Chairman & Co-Founder Audio Precision, Inc.
Copyright 2013 Audio Precision, Inc. Audio Precision® is a registered trademark of Audio Precision, Inc.
Introduction • This 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 textbooks – Unfortunately I cannot disclose certain revelations for competitive reasons – Our 1-hour time constraint will also limit the number of topics
• A copy of today’s slides can be obtained by contacting me at:
[email protected]
Selected Topics for Today • Taylor Series Model of Non-Linearity – Estimation of 2H & 3H distortion
• Resistors and Capacitors – Comparison of technologies – Non-linearity models and distortion estimation
• Op-Amps (circa 2013) – Bipolar versus JFET input stages – The 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 Distortion • Use 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 Distortion • A 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 100kΩ 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 Circuit
Note: Re = kT/qIe
Follower Distortion Estimation, cont’d • Dynamic emitter impedance, Re ≈ kT/qIe – “k” = Boltzmann’s constant = 1.38065E-23 – “T” = 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 = 11.138Ω An = 0.99713 – VB = 0.0 V: Ie = 3.576 mA, Re = 7.1085Ω Ao = 0.99816 – VB = +5.0 V: Ie = 4.870 mA, Re = 5.2200Ω 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 Output • The 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
Resistors in Analog Design
Linear Resistor Technologies • Composition • Thick Film • Thin Film or Metal Film • Metal Foil • Wire-Wound
• Some Comments about Matched Resistor Networks
Composition Resistors • The resistive element is a compacted mixture of carbon and ceramic held together in a resin base – Very popular prior to the 1970s, much less popular today – Still useful in some non-audio applications that require high peak power capability, or super low series inductance
• Unimpressive performance by today’s standards – Tolerances 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 Resistors • The resistive element is a conductive film applied to the surface of a cylindrical or rectangular substrate – Resistance is determined by film composition and etching pattern – Very wide variety of sizes and power ratings
• Very popular for general purpose applications – Tolerances of 2% to 0.1%, usually laser trimmed when
