MECH 373 Instrumentation and Measurements Lecture 4 Course

MECH 373 Instrumentation and Measurements Lecture 4 (Course Website: Access from your “My Concordia” portal) Measurement Systems with Electrical Signals (Chapter 3) • Electrical signal measurement systems • Signal conditioners Amplification Attenuation Filtering Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 1

Components of Measurement Systems Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 2

Electrical Signal Measurement Systems • Measuring systems that use electrical signals to transmit information between components have substantial advantages over completely mechanical systems. • Almost all modern engineering measurements can be made using sensing devices that have an electrical output. • In such devices, the measurand causes a change in an electrical property of the device (e. g. resistance, capacitance or voltage), either directly or indirectly. • Electrical output sensing devices have several significant advantages over mechanical devices: 1. Ease of transmitting the signal from measurement point to the data collection point 2. Ease of amplifying, filtering, or otherwise modifying the signal 3. Ease of recording the signal • However, completely mechanical devices are sometimes still the most appropriate measuring systems. Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 3

Signal Conditioning There are many possible functions in the signal-conditioning stage. Some of the common functions are: • Amplification • Attenuation • Filtering • Differentiation • Integration • Linearization • Combining a measured signal with a reference signal • Converting a resistance to a voltage signal • Converting a current signal to a voltage • Converting a voltage signal to a current signal • Converting a frequency signal to a voltage signal Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 4

Why Need Signal Conditioning? • Large amplification for small signals • Good transient response (i. e. small time constants) These are difficult to do with purely mechanical elements - due to friction and inertia! Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 5

General Characteristics of Signal Amplification • Signals in the millivolt range are common, and in some cases, signals are in microvolt range. • It is difficult to transmit such signals over wires of great length, and many processing systems require input voltage on the order of 1 to 10 V. • The amplification of such signals can be increased using a device called an amplifier. • The low-voltage signal, Vi, is amplified to a higher voltage, Vo. • The degree of amplification is specified by a parameter called the gain, G. Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 6

General Characteristics of Signal Amplification • Common instrumentation amplifiers usually have values of gain in the range 1 to 1000; however, higher gains can readily be achieved. • The term gain is often used even for devices that attenuate a voltage (i. e. Vo < Vi). • Hence, values of gain can be less than unity. • Gain is more commonly stated using a logarithmic scale, and the result is expressed in decibels (d. B). For voltage gain, it is expressed as: • For example, an amplifier with a gain (G) of 10 would have a decibel gain (Gd. B) of 20 d. B, and an amplifier with a gain of 1000 would have a decibel gain of 60 d. B. • If a signal is attenuated, that is, Vo is less than Vi, the decibel gain will have a negative value. Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 7

General Characteristics of Signal Amplification • Although increase in signal amplitude is the primary purpose of an amplifier, an amplifier can affect the signal. For example, frequency distortion, phase distortion, etc. • Typically a signal contains a range of frequencies. However, most amplifiers do not have the same value of gain for all frequencies. • For example, an amplifier might have a gain of 20 d. B at 10 k. Hz and a gain of only 5 d. B at 100 k. Hz. • Frequency response of a typical amplifier is shown in the following figure. In the figure, the decibel (d. B) gain is plotted versus the logarithm of the frequency. (Filter , 6 d. B per octave – next lecture) Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 8

General Characteristics of Signal Amplification • Typically, the gain has a relatively constant value over a wide range of frequencies. • However, at extreme frequencies, the gain is reduced (attenuated). • The range of frequencies over which the gain is almost constant is called the bandwidth. • The upper and lower frequencies defining the bandwidth are called corner or cutoff frequencies. The cutoff frequencies are defined as frequencies where the gain is reduced by 3 d. B. - Filter An amplifier with a narrow bandwidth changes the shape of an input time -varying signal by an effect known as the frequency distortion. Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 9

General Characteristics of Signal Amplification • Gain of an amplifier is relatively constant over the bandwidth, another characteristic of the output signal called the phase angle may change significantly. • If the voltage input signal to the amplifier is in the form of a sine wave and expressed as Vi(t)= Vmi sin (2πft) where, f is the frequency and Vmi is the amplitude of the input sine wave. • The output signal will be Vo(t) = GVmi( 2πft +φ ) where, φ is called the phase angle. Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 10

General Characteristics of Signal Amplification • Figures of amplitude response and phase response together called Bode diagram or Bode plot. • Pure sinusoidal waveforms, the phase shift is usually not a problem. Complicated periodic waveforms, it may result in a problem called phase distortion. • Phase angle varies linearly with frequency, waveform shape will not be distorted and it will only be delayed or advanced in time. • Phase angle varies nonlinearly with frequency, the shape of the waveform gets distorted. Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 11

General Characteristics of Signal Amplification Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 12

Input Loading and Output Loading • Input loading and output loading are potential problems. • Occur when using an amplifier. • Using many other signal-conditioning devices. • Input voltage to an amplifier generated: • Input or source device such as a sensor or another signal conditioning device. Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 13

Input Loading and Output Loading • Output voltage of the source device is altered: • When it is connected to the amplifier - a loading problem. • Amplifier output has similar problem, when it is connected to another device, i. e. the amplifier output voltage is changed. Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 14

Input Loading and Output Loading • Consider a source and an amplifier separately without being connected Rs = Sensor R Ri = Amplifier input R. Ro = Amplifier output R. • Now consider the combined system where the input source, amplifier and the output load are connected together Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 15

Input Loading and Output Loading • Source not connected to amplifier: • Voltage at the source output terminals will be Vs. • No current flowing through Rs. • Hence no voltage drop across Rs. • Source connected to amplifier: • Voltage at source output terminals will no longer be Vs. • Figure 3. 9, Vs, Rs and Ri form a complete circuit. • Current flowing through Rs. • Resulting voltage drop across Rs. • Amplifier has placed a load on the source device. Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 16

Input Loading and Output Loading • Similar behavior is observed when the output of the amplifier is connected to a device. • To minimize the loading effects at the input and output: • Ideal amplifier (or other signal conditioner) should have a very high value of input resistance (Ri). • Very low value of the output resistance (Ro). This can be seen from next slide. Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 17

Input Loading and Output Loading • To analyze this circuit, we will first solve the amplifier input voltage terms of the source voltage. The current through the input loop is and hence, in is given by: • Similarly, the voltage of the output loop, is given by: • Substituting first equation into the second equation, we get • If , the above equation will be approximated as • This is the equation of an ideal amplifier, that is, no loading effects. Lecture 4 Lecture Notes on MECH 373 – Instrumentation and Measurements 18