ABE425 Engineering Measurement Systems ABE425 Engineering Measurement Systems Measurement Systems with Electrical Signals Dr. Tony E. Grift Dept. of Agricultural & Biological Engineering University of Illinois

Agenda 1.AC and DC signals 2.Transducers 3.OpAmps 4.Active Filters 5.Loading error examples

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?

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

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

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!

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

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

Combined model of (a) input source, (b) amplifier and (c) output load You want to prevent loading errors Choose R i high Choose R o low

Non-inverting OpAmp

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

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

Inverting OpAmp

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

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

Integrating Inverting OpAmp : Virtual ground

Differentiating Inverting OpAmp: Virtual ground

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:

An instrumentation amplifier has two 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

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

Decibel notation Addition is much simpler than multiplication Notation in Bel (after Alexander Graham Bell) For Power For Voltages (Power ~ Voltage 2 ) In deciBel (0.1 Bel)

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

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

Chebyshev filters have sharp roll offs but lots of ripple

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

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

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

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

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

Active High-Pass filter analysis Without CIn general with impedances

High-pass and low pass section separated by OpAmp

Bandwidth and Distortion

Digital voltmeters / scopemeter

Modern digital bench top scopes

ABE425 Engineering Measurement Systems ABE425 Engineering Measurement Systems Measurement Systems with Electrical Signals The End Dept. of Agricultural & Biological Engineering University of Illinois