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Ch 3 Measurement Systems with Electrical Signals

Ch 3 Measurement Systems with Electrical Signals. ABE425Engineering . Agenda. AC and DC signals Transducers OpAmps Active Filters Loading error examples. AC and DC signals. Alternating Current (AC) Direct Current (DC) Most signals have both!

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Ch 3 Measurement Systems with Electrical Signals

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  1. Ch 3 Measurement Systems with Electrical Signals ABE425Engineering

  2. Agenda • AC and DC signals • Transducers • OpAmps • Active Filters • Loading error examples

  3. AC and DC signals • Alternating Current (AC) • Direct Current (DC) • Most signals have both! • DC component (offset) measurement: Put DMM on DC • AC component measurement: Put DMM on AC • Scope gives Amplitude and peak-peak value • To get the scope trace at 0: Put input on gnd. • How is the scope amplitude related to the AC value on the DMM?

  4. Let’s figure out what the AC RMS value is of this signal

  5. RMS value represents Power • DC: 12 Volt, R = 100 Ω • AC RMS value must give same power as DC of the same value • Mean value • Root Mean Square

  6. Question • If an AC Voltmeter shows 12V RMS • What is the amplitude of this signal? • Simple AC Voltmeters measure the amplitude and divide by sqrt(2) • This only works for Sinusoidal signals!! • True RMS voltmeters measure real Power, Resistance and take the square root of the ratio • This works for ANY signal since it follows the definition of the power equalization of DC and AC signals • The RMS value is NOT the mean of the AC signal. It is the Root of the Mean of the Squared value!

  7. Digital TRUE RMS meters digitize the signal and compute the RMS value from the definition • Digitize at least one cycle of the signal • Square it • Compute mean value • Integrate signal • Divide by cycle time • Take square root

  8. A Transducer converts a physical measurand into an electric signal • Antenna • Cathode Ray Tube. LCD monitor • Fluorescent light, light bulb. • Light Emitting Diode (LEDs) • Magnetic stripe cards • Photocells/Light

  9. Combined model of (a) input source, (b) amplifier and (c) output load • You want to prevent loading errors • Choose Ri high • Choose Ro low

  10. Non-inverting OpAmp

  11. Non-inverting OpAmp : Virtual ‘ground’ principle Since no current is flowing into the OpAmp: What is the input resistance for the source ?

  12. OpAmps have a limited band width (741 is about 1 MHz)

  13. f5_30 Inverting OpAmp

  14. f5_30 Inverting OpAmp: Virtual ground principle Since no current is flowing into the OpAmp: What is the input resistance for the source ?

  15. Capacitor equation Charge across Capacitor (Coulomb) Capacitance value (Fahrad (German for bicycle)) Voltage across Capacitor (Volt) Current through Capacitor (Ampere)

  16. f5_31 Integrating Inverting OpAmp : Virtual ground

  17. f5_31 Differentiating Inverting OpAmp: Virtual ground

  18. A buffer gives an near infinite input resistance and a near zero output resistance • This method can be used to prevent a loading error • Virtual ground principle:

  19. An instrumentation amplifier has twp high impedance (resistance) inputs • OpAmps have a very high input impedance (resistance) • This configuration has superb Common Mode Rejection Ratio (CMRR) up to 70 dB

  20. A simple way to attenuate a signal is by using a voltage divider

  21. Decibel notation • Addition is much simpler than multiplication • Notation in Bel (after Alexander Graham Bell) • For Power • For Voltages (Power ~ Voltage2) • In deciBel (0.1 Bel)

  22. Common filters arrangements are low-pass, high-pass, band-pass and band-stop (notch)

  23. Butterworth filters are smooth, but have a high roll-on roll-off factor.

  24. Chebyshev filters have sharp roll offs but lots of ripple

  25. Bessel filters are tame (no ripples) but a gradual roll off

  26. Active filters combine amplification and filtering in one circuit! What is the input impedance the source ‘sees’?

  27. Active Low-Pass filter analysis (1st order) Without C In general with impedances

  28. Notation differences • Wheeler / Ganji • System • frequency in Hz • Corner frequency • Grift • System • frequency in rad/s • Corner frequency rad/s • Time constant (s)

  29. Active High-Pass filter with OpAmp and Capacitor / Resistor pair (1st order) What is the input impedance the source ‘sees’?

  30. Active High-Pass filter analysis Without C In general with impedances

  31. High-pass and low pass section separated by OpAmp

  32. Bandwidth and Distortion

  33. The End

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