Today s menu. Last lecture. Series mode interference. Noise and interferences R/2 V SM Z L. E Th R/2. Voltage transmission system

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1 Last lecture Introduction to statistics s? Random? Deterministic? Probability density functions and probabilities? Properties of random signals. Today s menu Effects of noise and interferences in measurement systems. Noise sources and coupling mechanisms. Noise and interference reduction techniques. 1 2 Noise and interferences Series mode interference In a measurement system, we usually have a wanted signal (the measurement signal) and some unwanted signal The magnitude of the unwanted signal can sometimes be higher than that of the desired measurement signal! An unwanted deterministic signal is often referred to as an interference signal. Voltage transmission system V SM R/2 C i An unwanted random signal is often referred to as a noise signal. R/2 C 3 4

2 Noise and interferences (cont d...) -to-noise ratio Series mode interference (cont d...) Current transmission system The signal-to-noise ratio (or signal-to-interference) ratio, S/N (or SNR) is defined as ( ) ( ) S N =20log ETh WS 10 =10log V 10 db, SM W N i N Z N V SM R/2 C ii SM where W S and W N is the signal and noise power, respectively and and V SM are the r.m.s. values of the voltages. R/2 C 5 6 Common mode interference Common mode interference (cont d...) R/2 C i A common mode interference is caused by a potential offset on both sides of the circuit, relative to the common ground. If the impedance of the load is much higher than of the equivalent circuit, the voltage across the load is not significantly affected. V CM R/2 C 7 8

3 Noise sources Internal noise sources The Johnson noise: Voltage due to random temperature induced motion of electrons in resistors and semiconductors. Normally modeled as white Gaussian noise, with a power spectral density according to: φ(ω) =4 R k θ W/Hz, where θ is the absolute temperature (in Kelvins), R is the resistance (Ω), and k is the Boltzmann constant = J/K. Shot noise: Occurs in transistors, and is also often modeled as white noise. Noise sources (cont d...) External noise sources A.C. sources: The most common type of interference is the one originating from external power sources, operating at 240 V, 50 Hz. These can produce interfering sinusoidal signals in the measurement circuits. D.C. sources: The D.C. by itself generally doesn t produce any interference, but switching in these power supplies can give rise to a periodic impulse noise", that generate transient disturbances in the measurement system. RFI: Radio-frequency interference from oscillators in radio frequency transmitters/receivers nearby can get picked up by the system Coupling mechanisms Inductive coupling The figure shows inductive (electromagnetic) coupling between the measurement circuit and a nearby power circuit. ~ V AC i Power circuit M Coupling mechanisms (cont d...) Inductive coupling (cont d...) If the circuits are close enough, and there is a significant coupling M between them, the AC in the power circuit will cause a series mode voltage interference in the measurement circuit, according to Example V SM = M di dt If M =1μH and di/dt =10 3 A/s, then V SM =1mV. circuit 11 12

4 Coupling mechanisms (cont d...) Capacitive coupling Coupling mechanisms (cont d...) Capacitive coupling (cont d...) Power cable C V 50 Hz The capacitive (electrostatic) coupling results in a common mode interference voltage AND a series mode interference (see text book for derivation). B V CM = V E ( ) C 1 C 2 V SM = V B V E = 240 C 1 C 1E C 2 C 2E C 1E circuit C 2 E The series mode interference is only zero if the capacitances are perfectly balanced, i.e. C 1 = C 2 and C 1E = C 2E. C 2E Earth plane Noise and interference reduction Physical separation We have seen from the previous slides that: Mutual inductances (electromagnetic coupling), and coupling capacitances (electrostatic coupling) are present in most systems. These are inversely proportional to the distance between the circuits. Thus, effective reduction of these effects will be achieved if the distance is made large, whenever possible. Electromagnetic shielding A A B B Twisted pair wiring The size of the induced voltage depends on the orientation of the leads. Thus, in the ideal case, this configuration will result in a zero interfering voltage

5 Electrostatic screening and shielding The best way of avoiding electrostatic coupling is to enclose the entire measurement circuit in a grounded metal shield or screen. The screen is connected directly to ground at a SINGLE POINT. There is no direct connection between the circuit and the screen, but there will be a small leakage. The screen will provide an easy path for the interference, directly to ground. Use of differential amplifiers Differential amplifiers is a highly effective way of rejecting common mode interferences. R 1 V=V 1 CM ETh V CM R 2 - R F R F V OUT 0V In the ideal case, no common mode signal will remain. In practical cases, this is not true. See Chapter 9 for details Filtering V N Noise Consider the following noisy signal (with an additive cosine as interference). 1 I noise Gs () Filter O noise Time, t (s) 19 20

6 The signal from the previous slide, has the following spectrum. Power Spectrum Magnitude (db) Frequency After applying a suitable lowpass filter, the signal has the following spectrum. Power Spectrum Magnitude (db) Frequency And the result... s filtered signal original signal Time, t (s) Depending on the nature of the interference, lowpass, highpass, bandstop or notch filters could be applied. If the interference/noise and signal have non-overlapping spectra, almost complete noise rejection is accomplished. See text book for examples of filter spectra

7 Modulation Modulation (cont d...) If we know where a bandlimited disturbance enters the system, we can shift our desired signal s spectrum BEFORE. and then apply a bandpass filter. V N Band-limited Noise The shifting can be done by modulation, i.e. by multiplying the signal with a carrier frequency. x I noise Gs () Bandpass filter O Modulating carrier cos( ft) c Averaging If a signal is corrupted with additive noise (for example white Gaussian noise), and we can make multiple measurements of the same quantity, the noise can be significantly reduced by averaging. Why? Consider the following y(t) =x(t)e(t), where x(t) is the desired signal and e(t) is additive white Gaussian noise, with zero mean and variance σ Averaging (cont d...) Averaging N repetitions, we obtain ȳ(t) = 1 N N (x(t)e n (t)) n=1 = x(t) 1 N ē(t). Now, since each realization of e(n) is different, but the mean is zero, the mean of the average noise will also be zero. However, the variance of the average will be σ 2 ē = 1 N σ2, i.e. a significant reduction in noise variance (and thus noise power). This increases the signal-to-noise ratio. 28

8 Autocorrelation Read on your own. Summary Effects of noise in measurement systems. Noise sources and coupling mechanisms. Noise and interference reduction techniques Next lecture Deflection bridges (Ch. 9.1) Resistive sensing elements (Ch. 8.1) Recommended exercises

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