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Electrical measurements Measurements Believe nothing until you understand the measurement technique. Critical to all measurements All instruments have their own impedances and their own limits. Worry about: Main questions about instrument: Disturbing the system you study 1- Does it perturb the circuit (change the current paths noticeably)? Adding extra electrical signals Eliminating/reducing noise from measurements 2- How fast does it respond (what’s the bandwidth)? 3- How accurate is it (and how do you know)? Electrical measurements MTSC735, Spring 2008 1 “Voltmeter” and oscilloscope C 2 “Bandwidth” (and Fourier space) Measurement: take energy out of system to change readings of meter -- inherently disturbs the system. Vin Electrical measurements MTSC735, Spring 2008 R V Meter performance should exceed the Circuit performance Rs Vout Rsh ω meter “Gain-Bandwidth product” not the criterion, since both V range and ω range must be adequate. L * Are Rsh and Rs much larger than circuit impedances? If not then currents are perturbed. Read the specs and the instructions for instruments. * Can the meter respond faster than the circuit voltages changes? If not it is not much use. MTSC735, Spring 2008 Electrical measurements 3 MTSC735, Spring 2008 Electrical measurements Voltmeter or oscilloscope Sensor jargon Large to extremely high Zin (“Iin = 0”) Never assume that it’s “not loading” the circuit A sensor / transducer is a device that converts energy from/to some other form (e.g. heat, pressure, etc), into/from electrical signals 4 Sensitivity: minimum input that makes a detectable output change Dynamic Range: ratio of maximum and minimum values of input Analog (d’Arsenval meter): uses current through inductor to move needle. Slow (1Hz) and inaccurate (10-50%) Digital meter: numerical “readout” of voltage drop across big resistor. MUCH more precise (1/1000 – 1/107) and accurate (if calibrated) but very slow (0.1Hz). Usually very high input impedance. Oscilloscope: Draws a V(t) graph on screen. Faster (> 10 GHz) and reasonably accurate (2-5%). Digital scope is a little slower (1GHz) but much more precise (1/256 up to 1/65536). Either high input imperdance or matched to 50Ω for high frequencies. MTSC735, Spring 2008 Electrical measurements Precision: degree of reproducibility of the measurements Accuracy: degree to which you can calibrate the output Resolution: smallest detectable change in input (sensitivity + noise) Offset: sensor output that exists when it should be zero Linearity (calibration) error: difference between the output and the ideal theoretical curve Hysteresis: difference for increasing and decreasing values of input Response time: time required for the output to settle to a final value Sensor error: uhm, duh….. 5 MTSC735, Spring 2008 Electrical measurements 6 1 Bridge to measure small deviations Output from bridge is zero if Z1 Z2 = Z3 Z 4 so turn up the gain and look for small deviations from zero caused by small changes in one of the impedances. Design your sensor to incorporate the bridge Z1 Z3 Arrange circuits to balance out spurious noise and to measure only changes of interest. For example, in the accelerometer the equilibrium position is set be zero by placing the weight in symmetric position between coil windings. Circuit designed to have zero output at equilibrium. Z2 Z4 Can use AC drive and “lock-in” detection to see one part in ten million change. MTSC735, Spring 2008 Electrical measurements 7 MTSC735, Spring 2008 What could go wrong? Two-probe measurement Detector sensitivity and stability Current flow through the wires Electrical measurements 8 Electrical measurements 10 leads to voltage drop and Stability of “standard” resistors extra resistance measured by the meter. Self-heating in any resistors Rmeasured = Rx + Rlead1 + Rlead2 Thermal EMF or other contact potential Quick and cheap so OK if R lead is small enough Contact resistance to Rx Electrical measurements 9 Four-probe measurements MTSC735, Spring 2008 What is noise? Even in a perfect circuit, the ambient signals (radio, power lines, flourescent lamps, … will be picked up and convolved with the instruments signals. No current flows through wires to voltmeter so Rlead is On top of pick-up, there is always noise caused by the components of the instruments. eliminated from the Component noise has three sources: measurement. (1) Johnson (thermal) noise = random excited motion of charges (ΔV)2 = 4kB TR (Δω) (2) Shot (popcorn) noise = extra bursts of electron population (ΔI)2 = 2qIDC (Δω) (3) Flicker (1/f) noise = random changes of resistivity of materials (ΔV)2/(Δω) ∝ 1/ω More expensive but much more reliable. ln(ΔV) MTSC735, Spring 2008 Δω 60Hz 120Hz ln(ω) Noise in different components is uncorrelated so noise signals add up: (ΔVtotal)2 = (ΔV 1)2 + (ΔV 2)2 + (ΔV3 )2 + … MTSC735, Spring 2008 Electrical measurements 11 MTSC735, Spring 2008 Electrical measurements 12 2 ln(ΔV) How to avoid noise Measure of useful signal to noise signal: Since (ΔV)2 ∝ (Δω), just limit the bandwidth of the input. & V2 # SNR = 10 log10 $$ s 2 !! % Vn " Δω Connect wires and shield them to prevent pick-up. (could use simpler forms like Vs/Vn, in friendly conversation) Circuits can be characterized by how much worse they are than a perfect circuit with the same impedance and hence same Johnson noise. So define noise figure relative to Johnson noise (ΔV)2 = 4kBTR (Δω) 60Hz Connect “grounds” wisely to avoid forming big “ground loops” that pickup power line noise or act as antennae. 2 & 4k TR + Vn 2 # & Vn # NF = 10 log10 $$ B s !! = 10 log10 $$1 + 4k TR !! 4 k TR B s B s " % " % ln(ω) 120Hz Use averaging or phase-sensitive (lock-in) detection to increase signal to noise ratio. Use low noise components. Sometimes recast this as a noise temperature with Be aware of noise “sweet spots” in components and optimize circuit functions. & T # NF = 10 log10 $1 + n ! T" % Usually the more components you add, the worse it gets… 13 Noise sweet spots Total noise in any component is sum of Vtotal2 = Vn2 + (I nRs )2 Transistor model with voltage and current noise Vn Every component (especially active ones) adds noise. Rs Each will add both current noise and voltage noise. All noise terms depend on device current and on frequency. In ∝ I Pick operating point where added noise is smallest. Vs Design circuits to be operated where the net output noise is minimum. 14 2N5087 VCE= -5V In ( pA/Hz1/2) Noise in Components Electrical measurements MTSC735, Spring 2008 Vn (µV/Hz1/2) Electrical measurements MTSC735, Spring 2008 In ( pA/Hz1/2) IC ( mA) Remember: at the input gets amplified. 1 /f frequency Electrical measurements MTSC735, Spring 2008 What about real life? G Vin D S RG Electrical measurements 16 After careful choice of circuit components and operating points, connect them together and to the sensor and the transducer wisely. RD RB MTSC735, Spring 2008 Low noise circuit wiring VDD Each component has own noise contribution: V R = VS + ΔV n = IR + 4kBTR(Δω) + AR(Δω)/ω V C = I/jωC + ΔVn = I/jωC + ΔV1/f V DD = Videal + ΔVn Values in red depend on manufacturing details. (But most numbers are really small.) 15 Main point is to avoid spurious coupling of signals from outside the circuit: to avoid interference. Vout Two main modes of coupling: RS Make V ideal for resistors and capacitors by increasing current through components. Inductive (antenna) sensing of ambient E&M waves; Worse for AC than for DC. Φspurious Have to add them up and adjust component values, biases, etc to make best solution Capacitive sensing of proximate electrical fields. Can be worse problem for DC than for AC. BEST is choose components carefully and remember: input noise is amplified, Vspurious MTSC735, Spring 2008 Electrical measurements 17 MTSC735, Spring 2008 Electrical measurements 18 3 Wise wiring Lock-in, phase-sensitive detector AC signal driven through an unknown impedance can be detected with precision by multiplying it by the driving signal and average the product. Average automatically removes any signal not in phase with drive. Removes noise except in narrow range Δω near ω0. To avoid inductive coupling: twist wires together to make antenna cancel itself out. + – + – + – + – T V1 " V2 = or use high permeability shielding to block flux lines. # dt A sin($ t + % ) " A 1 1 1 0 sin($ 0 t + % 0 ) = 0 and capacitive problems Vin×Vref <Vin×Vref> ! multiplier Δω ln(ΔV) To avoid electrostatic coupling: use high permittivity “Faraday cage” to block electric field lines: Wires going to circuit General shielding idea Circuit of interest is same for both inductive 1 A0 A1& ($1 ' $ 0 )cos(%1 ' % 0 ) 2 (i.e. coax) 60 Hz Tiresome E/M fields MTSC735, Spring 2008 Electrical measurements 19 Phase sensitive detection In phase: 〈Vout〉 = Vrms 120 Hz ω0 Electrical measurements MTSC735, Spring 2008 ln(ω) 20 Spectroscopy (old school method) Out of phase: 〈Vout〉 = 0 Creates derivative of resonance peak Input signal Handy for servo-control circuits F(x) x Lock-in output (derivative) Zero crossing at resonance MTSC735, Spring 2008 Electrical measurements 21 Average to improve signal to noise Electrical measurements MTSC735, Spring 2008 22 Cross-correlation If possible to repeat from some reference point, then average many measurements. Measure the same thing twice and keep only the signals that appear in both. Vs /Vn = N1/2, so improvement is steady (but slow). Especially good for finding small, rare signals Great for removing random (uncorrelated noise), but useless for systematic (interference) problems. Vsupply,1 A1 Separate wires that generate, pick up noise “black” box that extracts only common signals A2 Vsupply,2 Voutput (" ) = lim T #$ MTSC735, Spring 2008 Electrical measurements 23 1 T & T 0 dtV1 (t)V2 (t % " ) Electrical measurements MTSC735, Spring 2008 24 ! 4