Dr Stephen Redmond School of Electrical Engineering & Telecommunications Ph: Rm: 458, ELECENG (G17)

Transcription

1 ELEC4623/ELEC9734: Semester 2, 2009 Dr Stephen Redmond School of Electrical Engineering & Telecommunications Ph: Rm: 458, ELECENG (G17) Notes: Session 2, 2009 ELEC4623/ELEC9734 1

2 Biomedical Instrumentation, Measurement and Design ELEC4623/ELEC9734 Lectures 7 & 8 Characteristics of Biological and Instrumentation Noise Session 2, 2009 ELEC4623/ELEC9734 2

3 The origins of noise Many sources of noise Only 4 principal sources that we need concern ourselves with Johnson (thermal) noise Shot noise Flicker noise Interference Session 2, 2009 ELEC4623/ELEC9734 3

4 Johnson s (Thermal) noise VRMS = 4 ktbr. Nyquist (1928) where k = Boltzman s constant (1.38 x J/K) T = Temperature (K) B = Bandwidth (Hz) R= resistance across which noise is measured (Ohms) Due to the random motion of electrons in the metallic lattice, a form of Brownian motion [Einstein 1905] Collisions of electrons between other electrons and with the lattice result in microscopically small currents with a Gaussian distribution Johnson noise has a uniform power spectral density (white noise); e.g. at 27 C, a 10kΩ resistor (over a 10 khz bandwidth) will exhibit a 1.29µV voltage due to Johnson noise Session 2, 2009 ELEC4623/ELEC9734 4

5 Shot Noise I = 2qI B RMS DC William Schottkey [1918] where q = Elementary charge (1.602 x C) B = Bandwidth (Hz) I DC = DC constant current (A) Due to the discrete nature of charge carriers in electric current Current is not a smooth flow, rather it is formed by the discrete flow of electrons which are subject to statistical fluctuations Shot noise is always associated with direct current flow In fact, it is required that there be DC current flow or there is no Shot noise Shot noise also has a uniform power spectrum Note: The derivation of the shot noise assumes the motion of any two electrons is uncorrelated In general, this will not be the case, and the noise level will be less than given by the equation Session 2, 2009 ELEC4623/ELEC9734 5

6 Flicker Noise (1/f noise, or pink noise) The origin of flicker noise is unknown It is known that t it has 1/f spectral density over a large range of frequencies. At cardiac frequencies (~1Hz) this can be significant and usually larger than shot noise MOSFETs have a higher ƒ c than JFETs or bipolar transistors (2 khz) Only with DC current Session 2, 2009 ELEC4623/ELEC9734 6

7 Interference Noise in electrical circuits can be caused by electrical, magnetic and electro-magnetic fields Such fields have many origins: TV, radio and satellite transmitters, cellular telephones, radar Transformers, garage door openers, motors, vehicle ignitions Power lines, computers, fluorescent and neon lights Atmospheric disturbances in ionosphere, lighting, cosmic radiation Microwave radiation from big bang Johnson, shot and flicker noise effectively limit the sensitivities we can achieve Interference, however, can be -and should be -actively avoided through design techniques Before application of filter! Session 2, 2009 ELEC4623/ELEC9734 7

8 Equivalent circuit for a noisy amplifier Total noise output voltage v = A ktr B + R i + e noise _ out 4 s s n n (in Volts rms) e n Noise voltage μv Hz Noise current i n e n l(l ) ,000 i n PA Typical (low noise pre-amp) noise Hz Note units! Freq.H Session 2, 2009 ELEC4623/ELEC9734 8

9 Signal to noise ratio ( SNR) o = 4kTR s E s B + e 2 n + R 2 s i 2 n From input From amplifier Noise Figure is the contribution of the amplifier to total noise SNRo Noise Figure (NF) = 20 log 10 SNR = 10log 10 i (R en + Rs in ) 1+ 4kTRsB df 0 dr = Putting s yields the optimum source resistance with minimum F R opt e i = n Ω n Noise Factor (F) = part in brackets i.e. NF = 10 log F Note: NF is a factor of R S and frequency Session 2, 2009 ELEC4623/ELEC9734 9

10 Earth and ground Ground and earth are not the same thing! Often they are connected together Circuit ground is also called zero volt reference (or just zero volts or reference) to avoid confusion Ground may be floating Battery powered devices Aeroplanes and automobiles Missiles etc. Ground Gou dand deat earth can beseea several kv different e if floating Session 2, 2009 ELEC4623/ELEC

11 Earth and ground Ground and earth are not the same thing Often they are connected together Circuit ground is also called zero volt reference (or just zero volts or reference) to avoid confusion Ground may be floating Battery powered devices Aeroplanes and automobiles Missiles etc. Ground Gou dand deat earth can beseea several KV different ee if floating Session 2, 2009 ELEC4623/ELEC

12 Earth connections Active 11kV 240V 240V ELCS Neutral Eart h ~ few ohms resistance Switchboard on side of house Copper/Aluminium rod An earth connection is formed by driving a copper or aluminium bar into the earth A good connection can result in a path resistance of just a few ohms Connections to earth are made for basically three reasons Protection from lightning strikes Prevent build-upup of static electricity which can cause instrumentation and devices to malfunction Prevent exposed conductors from becoming active (due to a fault) and posing an electrical shock hazard Session 2, 2009 ELEC4623/ELEC

13 Interference Noise There are three factors to consider: Noise source Coupling medium Receiver To solve the interference problem, it is necessary to remove, reduce or divert one or more of these factors Session 2, 2009 ELEC4623/ELEC

14 Noise Sources 50 Hz (power line) Switching transients (in switching regulators, solenoids and relays on power lines, from motors, on digital (i.e. TTL) lines, etc. Radar Pulses TV and radio transmission, mobile phones, oscillating equipment, walkie-talkies, paging systems, etc. Triboelectric ( static ), piezoelectric, etc. Session 2, 2009 ELEC4623/ELEC

15 Coupling medium Common impedance Electric field (capacitive) Magnetic field (inductive) EM field (antenna) Session 2, 2009 ELEC4623/ELEC

16 Receiver Usually noise is coupled into the front end of the pre-amp Signals here experience the most gain The first stage usually has highest h source impedance so is more prone to induced noise voltages (e.g. Johnson noise) it could be anywhere in the amplifier if exposed to a coupling medium Session 2, 2009 ELEC4623/ELEC

17 Noise coupling common impedance The noise current from circuit A develops a voltage across Z, which is presented as noise to circuit B Typically this may be a pulse train (digital circuitry) with a rate set by the operations o in circuit cu A (see next slide) Session 2, 2009 ELEC4623/ELEC

18 Noise coupling common impedance i noise v noise resistive v noise RLC This repetition rate will point to the source of the noise The waveform of the noise will help identify the impedance Z If it is resistive, the waveform will be the same as the noise current 1 If RLC it will tend to ring at a frequency and decay at a rate 2π LC set by L/R

19 Noise coupling Capacitive C S V noise = v Z + Z 1 jωc s Stray capacitance (C s ) couples noise voltages, particularly fast rising or falling edges or high frequencies, into high impedance circuits it typical for inputs to pre-amps Example: TTL circuit with typical rise time of 10 ns and a voltage swing of 5 V. If Z = 1 M ohm resistor, a C s of 0.1 pf will give 5 volt spikes! Session 2, 2009 ELEC4623/ELEC

20 Noise coupling Magnetic i (noise source) Z v noise induced emf (not much influenced by Z) V noise = 2πfBAcosθ x 10-8 Volts Where B = rms value of magnetic flux density (gauss G) A = area of the closed loop linking B (m 2 ) θ = angle of B to area A f = frequency (Hz) Example: Two conductors 1 foot long separated by 1 inch, in a 10 gauss 50 Hz field (e.g. near transformer or fan) leads to noise voltage of up to 3mV (depends on mutual inductance) Session 2, 2009 ELEC4623/ELEC

21 Reducing Interference Noise Keep cable lengths short For differential connections keep them equal and close together Reduce the area of loops twist t wires togetherth Separate low level signal wires from noisy ones Keep analogue and digital grounds separate Don t connect individual shields to ground at more than one point Connect each signal s cable shield to that signals reference potential (see figure on right) driving the shield If necessary use a screened room to block high level interference Don t allow the leads to move to avoid triboelectric (e.g. rubbing), piezoelectric effects or flux cutting Where such cables must cross, allow them to cross at right angles and with maximum separation Session 2, 2009 ELEC4623/ELEC

22 Environmental noise Session 2, 2009 ELEC4623/ELEC

23 Methods of interference coupling Common impedance coupling Capacitive coupling (electric field) Inductive coupling (magnetic field) Electromagnetic coupling (EM waves) Session 2, 2009 ELEC4623/ELEC

24 Common Impedance coupling i 2 i 1 2 i 1 V 1 V 2 R 1 R 2 R 1 V 1 R V2 R R + R 2 R and This is equivalent to: V 2 i 2 R 2 Two or more sources share a common impedance R so affect each other V R R + 1 R 1 R Session 2, 2009 ELEC4623/ELEC

25 Earth (ground) loops Another form of common impedance coupling is due to earth connections that have different potentials Currents in earth wires cause these differences in earth potentials If the circuit is an amplifier it will amplify the voltage difference in the earths Use careful layout (including single point grounds) Session 2, 2009 ELEC4623/ELEC

26 Capacitive coupling From electric fields When interference is introduced via stray capacitances Stray capacitances exist between all unshielded conductors The effects of capacitive coupling can be minimised by shielding and guarding shielding with conductive metal as barrier (absorption and reflection loss) e.g. 240V V C Power lines i stray R Session 2, 2009 ELEC4623/ELEC

27 Inductive coupling From magnetic fields Interference is introduced via mutual inductances Remember inductive noise is proportional to BA Easily distinguished because it varies with the area and orientation of the loop formed by the measurement cables Can be reduced by: reducing loop area (twisting cables) reducing magnetic field strength (magnetic shielding), but not always possible 240V V Power lines R Session 2, 2009 ELEC4623/ELEC

28 Electromagnetic coupling V R can be equivalent to V R Via electromagnetic waves Occurs when part of circuit acts as an antenna Caused by nonlinearities in input circuit demodulating RF signal and being amplified Fix by capacitive path to ground on input stage and/or source chokes (inductors) Session 2, 2009 ELEC4623/ELEC

29 Common mode problems In HF circuits, common mode problems can arise due to earth points having different potentials Power line C a In the LF bio-potential circuits, the major source of common mode (CM) signal is capacitive coupling of the 50 Hz mains onto the patient C b Session 2, 2009 ELEC4623/ELEC

30 Why common mode is a problem in ECG recording? ECG recorded as a Differential voltage (voltage difference of two inputs) Lead I: VI = VLA VRA Common mode voltage is present at both inputs (e.g. 50 Hz power line interference) To get ECG, the amplifier needs to have high h gain to differential signal and low gain to common mode signal, or high common mode rejection ratio (CMRR = differential gain/common mode gain) Session 2, 2009 ELEC4623/ELEC

31 Common mode noise If C a = 3pF, C b = 300 pf, then common mode noise V P = 2.4V MAINS ACTIVE 240V BUT if 240 V active wires near 50 Hz pot! on patient is C a patient, could have C a = 30 pf, Ca Vp = 240 hence V P over 20 volts Ca + This noise is common to any electrode placed on body If the biopotential input signal is + 1mV say, then a CMRR of 200,000 or V P db is required to have the output noise only 10% of the signal C b Cb Q: How is this CMRR calculated? Session 2, 2009 ELEC4623/ELEC

32 Common mode model of biopotential amplifier Z 1 Z a V c v 1 v Z 2 b Z 2 Z d Z' Z c Z c Z a Z b Z s Leads are shorted here (to get common mode (CM) signal) Suppose the gain to a CM signal if V 1 = V 2 is A c and the gain to a differential signal is A d. The ratio A d /A c is the CMRR CMRR = A d /A c typically CMRR ~ 100,000 = 100dB for an IC instrumentation amplifier Session 2, 2009 ELEC4623/ELEC

33 Common mode voltage What if Z 1 Z 2? Unequal impedances in inputs to differential amplifier will cause V 1 V 2, or V d = V 1 V 2 even if same common mode input Vc This is called the voltage divider effect The common mode voltage V C becomes a differential signal V d This differential i signal will be amplified by the differential gain A D of the amplifier. If Z s >> Z +Z c+z 1 and Z 2 then V d 0 How? Z a Z' Z b Z 1 Z a V c v 1 v Z 2 b Z 2 Z c Z c Z s Amplifier common Zc Zc Vd = V c Z 1+ Z c + Z s + Z ' Z 2 + Z c + Z s + Z See notes for derivation Z d ' Session 2, 2009 ELEC4623/ELEC

34 Reducing mains interference Several ways: Make Z S large e.g. by using a battery powered device Make Z C large and >>> Z 1 and Z 2. There is a limit to the size we C can make Z C as it must provide a DC path for bias currents of amplifier Match Z 1 and Z 2 Match the pair of electrodes and lead wires as much as possible (material, size) Often cannot control this as they are caused by electrode models Add a third electrode to make amplifier common = body potential (driven right leg electrode), so minimal current flowing through Z 1 or Z 2 to Z C Cannot just connect body directly to ground due to possibility of electrocution (note if body grounded Z b is shorted and V C =0) Session 2, 2009 ELEC4623/ELEC

35 Three electrode CM model V CM is not zero due to finite impedance Z rl The body displacement current flows through Z rl to set up V CM See Metting Van Rijn et al. Session 2, 2009 ELEC4623/ELEC

36 Driven right legs (DRL) z e z e average g of input signals Q: Purpose of R o? C f b R i - z r l R o + Amp. Common Due to potential divider effect and finite impedance of Z rl we instead use a drivenrightlegcircuittoreducev right to reduce CM We use an additional amplifier to actively drive the body common mode potential to be the same as amplifier common This forms a negative feedback loop stability problems C fb is used rather than a resistor to prevent instability The overall effect is to reduce effective Z rl by the loop gain at 50Hz In turn leads to lower V CM (more on this in next lecture) Session 2, 2009 ELEC4623/ELEC9734

37 Electric cable shielding Non-shielded inputs (see left) pick up large interference from potential divider effect of capacitive coupling Shielded inputs effectively reduces input to mains capacitance to zero by blocking the electric field However, they also introduce an increased capacitance to the circuit ground due to the input-to-shield to capacitance Session 2, 2009 ELEC4623/ELEC9734

38 Electric field interference Reduce the input-to-shield capacitances to negligible values by driving the shield This is called guarding the input - + average of input signals Session 2, 2009 ELEC4623/ELEC

39 Cable shield guarding 100Ω Ω 10kΩ Drive shield with low impedance (buffered) signal flowing in signal wire If ΔV = 0, then Q = 0, and effectively C 1 is discharged and has no effect NOTE: need to drive shield with voltage slightly less than signal to reduce possibility of instability and oscillation in DRL circuit Solution is expensive, need additional op-amp for each lead In practice we usually drive all shields with the AVERAGE of all input signals (the common mode voltage V cm ) see previous slide Session 2, 2009 ELEC4623/ELEC9734

40 Brute force analogue notch filters Simple twin T notch filter - R C R + v out v in C R 2 C Sometimes we cannot eliminate 50 Hz/60 Hz with other techniques We can use analogue notch filters to remove noise High quality ECG usually from Hz (and higher) Twin T circuit above has low Q Session 2, 2009 ELEC4623/ELEC

41 High Q notch filter - R R + vou t v in C C R 2 C Feedback - + Ratio H(f) Amplitude H(f) = H{f} e -i φ 1. 0 f/f g Discrete analogue notch filters are not recommended for modern designs Cannot easily switch between 50/60 Hz Depend upon component tolerances for accuracy Large board real estate and cost (especially for multi-channel) Single IC high-q notch filters are available if hardware filter is necessary Switched capacitor designs: inherent clock noise Continuous time active filter ICs (e.g. MAX274): no clock noise But use a software filter if you can! Session 2, 2009 ELEC4623/ELEC

42 Electrostatic shielding Before After This is the most common method of shielding equipment from electric and electro-magnetic (EM) fields The addition of the conductor dramatically affects the electric field The electric field causes a charge separation on the surface of the conductor, but electrical neutrality is maintained (net enclosed charge is 0 from Gauss s law) A conductive metal box effectively shields the inner volume from interference from external fields Session 2, 2009 ELEC4623/ELEC9734

43 Electrostatic shielding Shield can also trap an field, No + E field preventing it from interfering with Q outside the anything outside of the box box providing it is grounded to make the complete system neutral A shield also provides protection from EM fields, providing the Magnetic fields can also be conductor is thick enough shielded with a metal shield This is because the depth of BUT the requirement here is not that it has to be an ideal penetration of an EM wave is conductor, but rather that it governed by the skin effect has a high mu value (i.e. Example: A 10 MHz wave will relative permeability) penetrate only 26 μm into an aluminium i shield, before being reduced to 37% of its original intensity Session 2, 2009 ELEC4623/ELEC

44 Electrostatic shielding Record ECG in a shielded room: shields patient + preamplifier from any external electric field Session 2, 2009 ELEC4623/ELEC

45 Rules of shielding #1 C 1 C 2 Shield C 3 Always connect shield to ground to avoid feedback Session 2, 2009 ELEC4623/ELEC9734

46 Rules of shielding #2 If a shield is earthed, connect circuit ground to the shield at the same point where the shield is earthed Otherwise may lead to current flow in ground loops since earth may not be same everywhere (see right) Session 2, 2009 ELEC4623/ELEC

47 Reduce loop area Loop in which magnetic fields can induce interference Magnetic fields are coupled via circuit loops, therefore important to reduce loop area Usually done by twisting the conductors i.e. twisted pair Session 2, 2009 ELEC4623/ELEC

48 Filtering power supplies The power mains are a common way for one circuit to interfere with another Most interference is in the form of voltage transients and spikes from starting and stopping of motors and other electrical equipment Lightning strikes can destroy equipment! Power supply filtering and surge protection is vital Session 2, 2009 ELEC4623/ELEC

49 Sensible circuit layout - + Interference producing sources (e.g. power transformers) and interference susceptible circuits (e.g. sensitive amplifiers) should be kept apart Example: You would never place a power transformer next to the magnetic head of a tape recorder You should also keep in mind other practicalities such as mutual capacitance between PCB tracks Keep high level output signals and TTL logic clocks away from inputs! non-zero ground track resistance Ground loops etc. Use star ground Session 2, 2009 ELEC4623/ELEC

50 References High quality recording of bioelectric events. I: interference reduction, theory and practice, A. C. Metting Van Rijn, A. Peper, C. A. Grimbergen. Med. & Biol. Eng. & Comput., , Session 2, 2009 ELEC4623/ELEC