Instrumentation Sensors Book

4.3 Types of Amplifiers	55
VD = Vout = A logC Vin/R1IR = A logC Vin − A logC R1IR	(4.25)

which shows that the logarithmic relationship between Vout and Vin, and A logC R1IR is an offset constant.

The relation between the transistor’s base emitter voltage VBE and the collector/emitter current (IC) is given by:

VBE = A logC IC/IR

(4.26)

Because the VBE of the transistor is also Vout, (4.23) and (4.26) can be combined to give:

VBE = Vout = A logC Vin/R1IR = A logC Vin − A logC R1IR

(4.27)

which shows that the logarithmic relationship between Vout and Vin, and A logC R1IR is an offset constant.

Combinations of resistors and nonlinear elements can be used in multiple feedback loops to match the characteristics of many sensors for linearization of the output from the sensor (see Section 15.2.2). Logarithmic amplifiers are commercially available from some device manufacturers.

Antilogarithmic amplifiers perform the inverse function of the logarithmic amplifier. Two versions of the antilogarithmic amplifier are shown in Figure 4.15. The circuit equations can be obtained in a similar manner to the equations for the logarithmic amplifiers.

4.3.6Instrument Amplifiers

Because of the very high accuracy requirements in instrumentation, op-amp circuits are not ideally suited for low-level instrument signal amplification, but require impedance matching. Op-amps can have different input impedances at the two inputs. The input impedances can be relatively low, tend to load the sensor output, and can have different gains at the inverting and noninverting inputs. Common mode noise can be a problem. An op-amp configured for use as an instrument amplifier is shown in Figure 4.16. This amplifier has balanced inputs with very high input impedance, low output impedance, and high common mode noise reduction.

R1	R1
VIN	VIN
−	−
+	+
VOUT	VOUT

(a)

(b)

Figure 4.15 Circuits of antilogarithmic amplifiers using (a) a diode, and (b) a PNP transistor.

56	Analog Electronics

R1

R3

R5

	−
Vin1	+

−

+

RA

		R2
		R4
	−	R6
Vin2	+

Vout

R1 = R2

R3 = R4

R5 = R6

Figure 4.16 Circuit schematic of an instrumentation amplifier.

Gain is set by RA. Devices similar to the one shown in Figure 4.16 are commercially available for instrumentation. RA is normally an external component, so that the end user can set the gain [8].

The output voltage is given by:

V

=

R5

2R1

+ 1

(

V

− V

IN1 )

(4.28)

out

IN 2

R3

RA

Figure 4.17 shows a practical circuit using an instrumentation amplifier, which is used to amplify the output signal from a resistive bridge. R6 is used to adjust for any zero signal offset. This circuit also can be used as a differential transmission line receiver, as shown in Section 14.4.2.

	R1
	R3	R5
	−
	+
RB1	RS	−
	RA	+
+V	R2
R	R4
	RB3
	B2	R6
	−

+

Vout

R1 = R2 R3 = R4 R5 = R6

Figure 4.17 Instrumentation amplifier used for offset adjustment and amplification of a signal from a bridge.

4.4 Amplifier Applications

57

4.3.7Input Protection

Amplifiers, like all ICs, are susceptible to damage from excessive input voltages, such as from input voltages that are larger than the supply voltages, electrostatic discharge (ESD), or EMI pickup [9].

The inputs of ICs are internally protected. However, the protection can give rise to leakage currents, so that the protection is limited. Typically, the overvoltage protection is limited to approximately ±8V greater than the supply voltages. That is, with a ±15V supply, the protection is ± 23V. The protection can be improved by the use of external resistors and clamps, if this is practicable.

Electrostatic discharge is the biggest problem, particularly for CMOS devices, because of their high input impedance. There are two main sources of ESD. The human body can generate a large amount of static energy, which can destroy a device just by handling it. Hence, there is the need for ground straps when handling ICs. The other source of ESD, which can be as high as 16 kV, is from equipment. The human body and equipment ESD model is given in MIL-STD 883B (military standard), and similar models are given in the IEC 1000.4.2 standard.

EMI normally can be reduced to an acceptable level by capacitive filtering at the input to the IC.

4.4Amplifier Applications

The stage gain of an op-amp with feedback is limited to about 500, primarily by feedback resistor values, as well as from amplifier considerations. For instance, an amplifier with a 5 kΩ input resistor would have a feedback resistor of 2.5 MΩ, which is comparable to the input impedance of the bipolar op-amp.

In process control, amplifiers are used in many applications other than signal amplification, filtering, and linearization [10]. Some of these applications are as follows:

•Capacitance Multiplier;

•Gyrator;

•Sine Wave Oscillator;

•Power Supply Regulator;

•Level Detection;

•Sample and Hold;

•Voltage Reference;

•Current Mirror;

•Voltage to Frequency Converter;

•Voltage to Digital Converter;

•Pulse Amplitude Modulation.

More information on the design and use of these circuits can be found in analog electronic textbooks.

58	Analog Electronics

4.5Summary

This chapter introduced and discussed integrated op-amps, and how their low drift characteristics make them a suitable building block for both low frequency ac and dc small signal amplification. However, op-amps are not ideal amplifiers because of the mismatch at the inputs, input impedance, and different gain at the inputs. The high open loop gain characteristics of the op-amp make it necessary to use feedback for stabilization, and the use of a set zero is required for adjustment of the input mismatch. The op-amp is a very versatile device, and can be used in many configurations for amplifying low-level voltages or currents, summing voltages, and converting between voltage and current. They also may be used as nonlinear amplifiers, as comparators, and for waveform shaping. The use of op-amps is not limited to signal amplification in process control; they have many other applications. Op-amps are susceptible to excessive supply voltage and ESD, so that care and protection is needed in handling.

References

[1]Mancini, R., Op-Amps for Everyone, 1st ed., Elsevier Publishing, 2003.

[2]Schuler, C. A., Electronics Principles and Applications, 5th ed., McGraw-Hill, 1999, pp. 221–238.

[3]Sutko, A., and J. D. Faulk, Industrial Instrumentation, 1st ed., Delmar Publishers, 1996, pp. 80–89.

[4]Wurcer, S. A., and L. W. Counts, “A Programmable Instrument Amplifier for 12 Bit Resolution Systems,” Proc. IEEE Journal of Solid State Circuits, Vol. SC17, No. 6, December 1982, pp. 1102–1111.

[5]Nash, E., “A Practical Review of Common Mode and Instrumentation Amplifiers,” Sensors Magazine, Vol. 15, No. 7, July 1998.

[6]Johnson, C. D., Process Control Instrumentation Technology, 7th ed., Prentice Hall, 2003, pp. 97–99.

[7]Humphries, J. T., and L. P. Sheets, Industrial Electronics, 4th ed., Delmar, 1993, pp. 5–8.

[8]Harrold, S., “Designing Sensor Signal Conditioning with Programmable Analog ICs,” Sensors Magazine, Vol. 20, No. 4, April 2003.

[9]Bryant, J., et al., “Protecting Instrumentation Amplifiers,” Sensors Magazine, Vol. 17, No. 4, April 2000.

[10]Humphries, J. T., and L. P. Sheets, Industrial Electronics, 4th ed., Delmar, 1993, pp. 46–70.

C H A P T E R 5

Digital Electronics

5.1Introduction

Digital electronics has given us the power to accurately control extremely complex processes that were beyond our wildest dreams a few years ago [1]. It would take many volumes to cover the subject of digital technology, so in this text we can only scratch the surface. There is a place for both analog and digital circuits in instrumentation. Sensors and instrumentation functions are analog in nature. However, digital circuits have many advantages over analog circuits. Analog signals are easily converted to digital signals using commercially available analog to digital converters (ADC). In new designs, digital circuits will be used wherever possible.

Some of the advantages of digital circuits are:

•Lower power requirements;

•Increased cost effectiveness;

•Ability to control multivariable systems simultaneously;

•Ability to transmit signals over long distances without loss of accuracy and elimination of noise;

•Higher speed signal transmission;

•Memory capability for data storage;

•Compatibility with controllers and alphanumeric displays.

5.2Digital Building Blocks

The basic building blocks used in digital circuits are called gates. The types of gates are Buffer, Inverter, AND, NAND, OR, NOR, XOR, and XNOR [2]. These basic blocks are interconnected to build functional blocks, such as encoders, decoders, adders, counters, registers, multiplexers, demultiplexers, memory, and so forth. The functional blocks are then interconnected to make systems, such as calculators, computers, microprocessors, clocks, function generators, transmitters, receivers, digital instruments, telephone systems, ADCs, and Digital to Analog Converters (DAC), to name a few.

Figure 5.1 shows the traditional logic symbols used together with the Boolean equation describing the gate function. The gates were originally developed using bipolar technology, but are now made using CMOS technology, which has the

59

60	Digital Electronics

	A	A
		Buffer
	A	C = A·B
	B
		AND
	A	C = A + B
	B
		OR
	A
	B	C = A B = A·B + A·B
		XOR

Figure 5.1 Traditional digital logic gate symbols.

	A	A
		NOT
	A	C = A·B = A + B
	B
		NAND
	A	C = A + B = A·B
	B
		NOR

A

B

C = A B = A·B + A·B

XNOR

advantages of low power requirements, small size, high speed, and high fanout, or the ability to drive a large number of gates.

The American National Standards Institute (ANSI) and the IEEE have developed a set of standard symbols for gates, which they are pushing very hard for acceptance. These symbols are given in Figure 5.2. Either set of logic symbols may be encountered in practice, so it is necessary to be familiar with both. A lesser-known third set of logic symbols was developed by the National Electrical Manufacturers Association (NEMA) [3]

To understand how a problem is analyzed to obtain a Boolean expression, consider the system shown in Figure 5.3. A storage tank is being filled with a liquid, and it is necessary to sound an alarm when certain parameters exceed specifications. We label the variables as follows: the flow rate is A, the humidity B, and the temperature C. Set points have been established for these variables, and depending on whether the variables are above or below the set points, a 1 or 0 is assigned to each variable, in order to develop the Boolean expression for the system. When the Boolean variable Y goes to the 1 state, an alarm will be activated. The conditions for turning on the alarm are:

•High flow with low temperature;

•High flow with high humidity;

	A	1	A	A	1	A
		Buffer			NOT
	A	&	C = A·B	A	&	C = A·B = A + B
	B			B
		AND			NAND
	A	≥1	C = A + B	A	≥1	C = A + B = A·B
	B			B
		OR			NOR
	A	=		A	=
	B		C = A B = A·B + A·B	B
						C = A B = A·B + A·B
		XOR			XNOR

Figure 5.2 ANSI/IEEE standard logic symbols.

5.3 Converters

61

		1 High
	Humidity	B =
		0 Low
		Temperature
	Flow	1 High	Alarm
	1 High	C =	1 On
		0 Low
	A =		Y =
	0 Low		0 Off

Figure 5.3 Setup to illustrate the development of a Boolean equation.

• Low flow with high humidity and low temperature.

Using these conditions, we can now define a Boolean expression that will give Y

=1 for each equation, as follows:

•Y = 1 = A·C condition 1

•Y = 1 = A·B condition 2

•Y = 1 = A·B·C condition 3

These three equations can now be combined with the OR operation, so that if any of these conditions exist, the alarm will be activated. This gives:

Y = A·C + A·B + A·B·C						(5.1)

This equation can now be used to define the digital logic required to activate the alarm system.

Example 5.1

Develop a digital circuit to implement the alarm conditions discussed for Figure 5.3, using the gate symbols given in Figure 5.1.

The starting point is the Boolean expression developed for Figure 5.3, which is (5.1).

Y = A·C + A·B + A·B·C

There are many gate combinations that can be used to implement this logic equation. One possible solution using AND and OR gates is given in Figure 5.4. Any equations or Boolean expressions should be simplified before implementation.

5.3Converters

We live in an analog world and sensor measurements are analog in nature. All of our computational functions, signal transmission, data storage, signal conditioning, and so forth, derive many benefits from the digital world. It is therefore necessary to convert our analog signals into a digital format for processing, and then back to

	62		Digital Electronics
	Flow		A·B
	A
	Humidity		A·B + A ·C
	B	C	A·C
	Temperature
			Y
	C		A·B·C

A

A·B

Figure 5.4 Solution for Example 5.1.

analog for final control. The interface between the analog world and digital world uses converters. An ADC changes the analog signal into a digital format, and a DAC changes the digital signal back to analog. The characteristics of these converters must be precise and accurately known, to establish the relationship between the analog and digital signal.

5.3.1Comparators

The simplest form of information transfer between an analog signal and a digital signal is a comparator. This device is simply a high gain amplifier that is used to compare two analog voltages, and depending on which voltage is larger, will give a digital “0” or “1” signal. This device is shown in Figure 5.5(a), with the input and output waveforms in Figure 5.5(b). The comparator is an integral part of ADCs and DACs, and of many monitoring devices.

One of the input voltages in this case, Va, is known as a fixed trigger level, a set level, or a reference voltage. The other voltage is the variable, which when compared to Va in a comparator, will give a digital “1” or “0” signal, depending on whether it is greater than or less than the reference voltage.

Example 5.2

A “1” signal is required to trigger an alarm, if the fluid level in a tank is more than 3m deep. The level sensor gives an output of 9.3 mV for every centimeter increase in depth. What is the required alarm voltage?

In this case, the sensor is connected to terminal Vb, and a reference level of 2.79V (9.3 × 100 × 3 mV) is connected to terminal Va in Figure 5.2(a).

Va	-			Inputs	Va
					Vb
			0	Va > Vb
Vb	+	Vout
			1	Va < Vb
					1
				Output
					0
		(a)				(b)

Figure 5.5 (a) circuit and (b) waveform basic comparators.

5.3 Converters

63

Hysteresis is obtained with positive feedback, as shown in Figure 5.6(a), and is often used in comparators to minimize or overcome noise problems. Some noise can be filtered out, but it is difficult to completely eliminate all of it. Noise can cause the comparator to switch back and forth, giving uncertainty in the trigger point. This is shown in Figure 5.6(b), where input Vb is varying as it increases due to noise. This input, when used in a comparator without feedback, gives several “1” level outputs as shown, which may cause problems when trying to interpret the signal. If positive feedback (or hysteresis) is used, as shown in Figure 5.6(a), then a clean output is obtained, as shown in the lower waveform in Figure 5.6(b). Positive feedback produces a dead band. Once the comparator has been triggered, the trigger point is lowered, so that the varying input must drop to below the new reference point before the comparator output will go low.

In Figure 5.6(a), the condition for the output to go high is given by:

Vb ≥ Va

(5.2)

After the output has been driven high, the condition for the output to return to low is given by:

Vb ≤ Va − (R1/R2)Vh

(5.3)

where Vh is the voltage of the output when high.

The dead band or hysteresis is given by (R1/R2)Vh, and therefore can be selected by the choice of resistors.

Example 5.3

In Example 5.2, if there are waves with amplitude of 35 cm due to pumping, what is the value of R2 to give a dead band with a 5-cm safety margin to prevent the comparator output from going low? Assume R1 = 5 kΩ, and output high = 5V.

The dead band is (35 + 5) × 9.3 mV = 37.2 mV

(R1/R2)Vh = 37.2 mV

R2 = 5 × 5/0.0372 kΩ = 672 kΩ

				Inputs	Va
Va			0		Vb
				Va > Vb
		Vout
	−		1	Va < Vb
	+			Without	1
Vb	R1			feedback	0
	R2			Output with	1
				feedback	0
	(a)				(b)

Figure 5.6 Comparator with hysteresis.

64	Digital Electronics

5.3.2Digital to Analog Converters

There are two basic methods of converting digital signals to analog signals: DACs, which are normally used to convert a digital word into a low power voltage reference level or waveform generation; and pulse width modulation (PWM), which is used to convert a digital word into a high power voltage level for actuator and motor control [4].

DACs change digital information into analog voltages using a resistor network or a current mirror method. Using either of these methods, the analog signals are low power and are normally used as a low power voltage level, but can be amplified and used for control. Using a resistor network, a DAC converts a digital word into an analog voltage by using the resistors to scale a reference voltage, resulting in a voltage value proportional to the value of the binary word. For instance, when the binary value is zero, the output voltage is zero, and when the binary number is at a maximum, the output is a fraction less than the reference voltage, which may be scaled up to give discrete output voltage levels. The output voltage (Vout) from a DAC is given by:

Vout = Vref (2 n−1 + − − − − +21 + 2 0 ) 2 n

(5.4)

For an 8-bit device, the maximum output voltage is Vref × 255/256 = 0.996 Vref, and for a 10-bit DAC, the maximum output voltage is Vref × 1023/1024 = 0.999 Vref, showing that the maximum output voltage is slightly less than the reference voltage.

In the 8-bit DAC, the reference voltage may be scaled up by 256/255 to give discrete output voltage steps.

Example 5.4

An 8-bit DAC has a reference voltage of 5V. What would be the voltage corresponding to a binary word of 10010011?

Vout = 5(128 + 16 + 2 + 1)/256V

Vout = 2.871V

A DAC is typically an IC in a black box, but it can be constructed from discrete components. It is usually more cost effective to use an IC, but it can be useful in some cases to understand the structure, which may have uses in other applications. A DAC uses either a resistive ladder network, which can be resistor ratios, such as R, 2R, 4R, or 8R, but in this method the resistors can get very large. For instance, if the lowest value resistor is 5 kΩ, then the spread for 8 bits is up to 1.28 MΩ. This wide spread in resistors leads to inaccuracies, due to the different coefficients of resistance with temperature at high and low resistor values. A more practical resistor network is the R-2R ladder, where only two values of resistor are required. A 4-stage ladder network is shown in Figure 5.7, where CMOS switches are used to switch the reference voltage (VR), and ground to the resistor network.

In an R-2R network, a Thévenin voltage source can be used to obtain the relation between the output voltage (Vout) and the voltage applied to the resistor (VR or 0). The output voltage is given by: