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

Components of Measurement Systems

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.

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

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!

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.

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 (dB). For voltage gain, it is expressed as: • For example, an amplifier with a gain (G) of 10 would have a decibel gain (GdB) of 20 dB, and an amplifier with a gain of 1000 would have a decibel gain of 60 dB. • If a signal is attenuated, that is, Vo is less than Vi, the decibel gain will have a negative value.

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 dB at 10 kHz and a gain of only 5 dB at 100 kHz. • Frequency response of a typical amplifier is shown in the following figure. In the figure, the decibel (dB) gain is plotted versus the logarithm of the frequency.

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 dB. An amplifier with a narrow bandwidth changes the shape of an input time-varying signal by an effect known as the frequency distortion.

General Characteristics of Signal Amplification • Although the 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.

General Characteristics of Signal Amplification • The figures of amplitude response and phase response together are called the Bode diagram or Bode plot. • For pure sinusoidal waveforms, the phase shift is usually not a problem. However, for complicated periodic waveforms, it may result in a problem called phase distortion. • If the phase angle varies with frequency, the amplifier can distort the shape of the waveform. • However, if the phase angle varies linearly with frequency, the shape of the waveform will not be distorted and the waveform will only be delayed or advanced in time. • But if the phase angle varies nonlinearly with frequency, the shape of the waveform gets distorted.

General Characteristics of Signal Amplification

Input Loading and Output Loading • Input loading and output loading are potential problems that can occur when using an amplifier (and when using many other signal-conditioning devices). • The input voltage to an amplifier is generated by an input or source device such as a sensor or another signal conditioning device. • If the output voltage of the source device is altered when it is connected to the amplifier, there exists a loading problem. • A similar problem occurs when the output of the amplifier is connected to another device, i.e. the amplifier output voltage is changed.

Input Loading and Output Loading • Consider a source and an amplifier separately without being connected • Now consider the combined system where the input source, amplifier and the output load are connected together

Input Loading and Output Loading • If the source is not connected to the amplifier, the voltage at the source output terminals will be Vs. This is because there is no current flowing through Rs and consequently, there will be no voltage drop across Rs. • When the source is connected to the amplifier, the voltage at the source output terminals will no longer be Vs. As shown in Figure 3.9, Vs, Rs and Ri form a complete circuit. Consequently, there will be a current flowing through Rs and a resulting voltage drop across Rs. That is, the amplifier has placed a load on the source device. • 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, an ideal amplifier (or other signal conditioner) should have a very high value of input resistance (Ri) and a very low value of the output resistance (Ro). This can be seen from next slide.

Input Loading and Output Loading • To analyze this circuit, we will first solve the amplifier input voltage in terms of the source voltage . The current through the input loop is and hence, 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.

Example – output loading • Consider Voltage Divide Circuit … if we stick a “VERY HIGH” impedance meter between terminals … no current flows from a to b and we can write …. I s I s

Example (contd) • What happens if meter impedance is not “Very High”? • Current Flows from a to b … circuit is “loaded” • Voltage drop from a to b Ib Ia RM • Current splits thru Ra and RM IM = 0

Example (contd) • Voltage drop through Ra and Rb Ib Ia • Solve for Ia RM IM = 0 • Solve for current thru meter

Example (contd) • Example Calculation … Ra = 1000  Rb = 1500  Vs = 15 V Ib 10M Ia RM = = 5.9996 10-7 amps OK … almost no current

Example (contd) • Example Calculation … Ra = 1000  Rb = 1500  Vs = 15 V Ib 10M Ia • Calculate Vab RM = = 5.9996 volts

Example (contd) • Example Calculation … Ra = 1000  Rb = 1500  Vs = 15 V Ib Ia • What happens if Meter has “infinite impedance” IM=0 RM = s = 6 volts • meter loading “insignificant”

Example (contd) • Example Calculation … Ra = 1000  Rb = 1500  Vs = 15 V How about If … RM = 10 k Ib Ia RM = = 5.66 volts • meter loading causes significant Error in voltage reading!