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Chapter 4 Sensor interface circuits
Prof. Dehan Luo
第四章 传感器接口电路
Section One Review of circuit theory（第一节 电路理论复习）
1、Voltage, current and resistance
2、Capacitance and inductance
3、Complex number representations（复数表达）
Section Two Measurement of resistance
（第二节 电阻传感器测量电路）
1、Voltage dividers（分压器）
2、Wheatstone Bridge（惠斯登电桥）
3、Temperature compensation for strain gauges
（应变片温度补偿）
Section Three AC bridges （第三节 交流电桥测量电路）
1、Measurement of capacitance （电容传感器测量电路）
2、Measurement of inductance （电感传感器测量电路）
Section Four operational amplifier circuits（第四节 运算放大器测量电路）
1、Inverting and non-inverting amplifier
2、Summing and differential amplifier
3、Integrating and differentiating amplifier
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Section One Review of circuit theory
第一节 电路理论复习
Voltage, current, resistance and power
1、Voltage
The voltage between two points is the energy required to move a
unit of positive charge from a lower to a higher potential. Voltage
is measured in Volts (V)
（电压是正电荷从低电位移到高电位所需要的能量，电压测量单位是伏特）
2、Current
Current is the rate of electric charge through a point. The unit of
measure is the Ampere or Amp (A)
（电流是电荷通过某点的速率，电流测量单位是安培）
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Voltage, current, resistance and power （Cont.)（续）
3、Resistance
Given a piece of conducting material connected to a voltage
difference V, which drives through it a current I，the resistance is
defined as（假设导电材料连接到电压差为V上，通过它的电流为I，
则该材料的电阻定义为）
（1）As you will recall, this is known as Ohm’s Law
（2）An element whose resistance is constant for all values of V
is called an ohmic resistor（在电压范围内，电阻值为常数的
元件被称为欧姆电阻）
（3）Series and parallel resistors…（电阻串联、并联….）
4、Power
The power dissipated by a resistor is（电阻消耗的功率是）
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Voltage, current, resistance and power （Cont.)（续）
5、Kirchhoff’s Laws（基尔霍夫定律）
（1）1st Law (for nodes) （第一基尔霍夫定律，节点定律）
The algebraic sum of the currents into any node of a circuit is zero
Or, the sum of the currents entering equals the sum of the
currents leaving.Thus, elements in series have the same current
flowing through them
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Voltage, current, resistance and power （Cont.)（续）
5、Kirchhoff’s Laws（基尔霍夫定律）（续）
（2）2nd Law (for loops) （第二基尔霍夫定律，回路定律）
The algebraic sum of voltages in a loop is zero.Thus, elements in
parallel have the same voltage across them.
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Capacitors and inductors
1、A capacitor is an element capable of storing charge
（1）The amount of charge is proportional to the voltage across the
capacitor （电容器的电荷量正比于电容器两端的电压）
Q=CV
C is known as the capacitance (measured in Farads)
（2）Taking derivatives（导出公式）
（3）Therefore, a capacitor is an element whose rate of voltage
change is proportional to the current through it（电容器是电压上升
速率正比于通过其电流的器件）
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Capacitors and inductors （Cont.) （续）
2、Similarly, an inductor is an element whose rate of current
change is proportional to the voltage applied across it
（电感中的电流增加的速率正比于加在它两端的电压）
L is called the inductance and is measured in Henrys
（L称为电感，单位为亨）
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Capacitors and inductors （Cont.) （续）
3、Frequency analysis
Consider a capacitor driven by a sine
wave voltage（电容器由正弦电压驱动）
（1）The current through the capacitor is
（2）Therefore, the current phase-leads the voltage by 900 and the ratio
of amplitudes is（电流相位超前电压相位90度，幅值比为）
（3）What happens when the voltage is a DC source?
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Voltages as complex numbers（电压表达的复数形式）
1、At this point it is convenient to switch to a complex-number
representation of signals
（在此，将信号转换成复数表达方式是方便的）
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Voltages as complex numbers（电压表达的复数形式）（Cont.)(续)
2、Applying this to the capacitor V(t)/I(t) relationship
（电容器上电压电流的复数关系）
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Voltages as complex numbers（电压表达的复数形式）（Cont.)(续)
3、
Impedance
Impedance (Z) is a generalization of resistance for circuits that have
capacitors and inductors
（阻抗是含有电容和电感电路的电抗的一般表达形式）
Capacitors and inductors have reactance, while resistors have resistance
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Voltages as complex numbers（电压表达的复数形式）（Cont.)(续)
4、
Ohm’s Law generalized（欧姆定律通用形式）
5、 Impedance in series and parallel（串、并联电路）
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Voltages as complex numbers（电压表达的复数形式）（Cont.)(续)
6、 High-pass filter
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Section Two
Prof. Dehan Luo
Measurement of resistance
第二节 电阻传感器测量电路
1、Voltage dividers（分压器）
2、Wheatstone Bridge（惠斯登电桥）
3、Temperature compensation for strain gauges
（应变片温度补偿）
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Voltage dividers（分压器）
Assumptions
Interested in measuring the fractional change
in resistance x of the sensor: RS=R0(1+x)
R0 is the sensor resistance in the absence
of a stimuli（ R0为无激励时的传感器电阻）
Load resistor expressed as RL=RK for convenience
The output voltage of the circuit is
Questions
What if we reverse RS and RL?
How can we recover RS from Vout?
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Voltage dividers （Cont.)（分压器）（续）
What is the sensitivity of this circuit?
For which RL do we achieve maximum sensitivity?
This is, the sensitivity is maximum when RL=R
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Wheatstone bridge
1、A circuit that consists of two dividers
A reference voltage divider (left)
A sensor voltage divider
2、Wheatstone bridge operating modes
（a）Null mode（零模式，即平衡电桥）
R4 adjusted until the balance condition is met:
Advantage: measurement is independent of fluctuations in VCC
（b）Deflection mode （偏差模式，即不平衡电桥）
The unbalanced voltage Vout is used as the output of the circuit
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Wheatstone bridge (Cont.)（续）
3、
Assumptions（假设）
（1）Want to measure sensor fractional
resistance changes RS=R0(1+x)
（2）Bridge is operating near the
balance condition
（电桥工作于接近平衡条件）
4、The output voltage becomes（输出电压为）
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Wheatstone bridge (Cont.)（续）
5、
What is the sensitivity of the Wheatstone bridge?（惠斯登电桥灵敏度）
The sensitivity of the Wheatstone bridge is the same as that of a
voltage divider
You can think of the Wheatstone bridge as a DC offset removal circuit
（惠斯登电桥可认为是直流偏置消除电路）
So what are the advantages, if any, of the Wheatstone bridge?
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Temperature compensation for strain gauges （应变片温度补偿）
1、 Strain gauges are quite sensitive to temperature
（1）A Wheatstone bridge and a dummy strain gauge may be used to
compensate for this effect（惠斯登电桥与补偿应变片可用来补偿温度效应）
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Temperature compensation for strain gauges （应变片温度补偿）（续）
（2） The “active” gauge RA is subject to temperature (x) and strain
(y)
stimuli（测量应变片感受温度X和应变Y）
（3）The dummy gauge RD, placed near the “active”gauge, is only
subject to temperature （测量应变片置于测量应变片附近，只
感受温
度X和）
（4）The gauges are arranged according to the figures below
（5） The effect of (1+y) on the right divider cancels out
（右侧分压器上的（1+y）被消除）
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Section Three AC bridges
第三节 交流电桥测量电路
1、Measurement of capacitance （电容传感器测量电路）
2、Measurement of impedance （电感传感器测量电路）
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AC bridges （交流电桥）
1、The structure of the Wheatstone bridge
can be used to measure capacitive and
inductive sensors （惠斯登电桥可用于电
容传感器和店感传感器的测量）
（1）Resistance replaced by generalized impedance
（2）DC bridge excitation replaced by an AC source
2、The balance condition becomes（平衡条件为）
which yields two equalities, for real and
imaginary components
（实部与实部，虚部与虚部分别相等）
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AC bridges（Cont.) （交流电桥）(续)
3、There is a large number of AC bridge arrangements
These are named after their respective developer
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Section Four operational amplifier circuits
第四节
运算放大器测量电路
1、Inverting and non-inverting amplifier
2、Summing and differential amplifier
3、Integrating and differentiating amplifier
4、Current-voltage conversion
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Inverting and non-inverting amplifiers
1、Non-inverting amplifier
2、Inverting amplifier
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Summing and differential amplifier （求和放大器和差动放大器）
1、Summing amplifier
2、 Differential amplifier
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Integrating and differentiating amplifier（积分与微分放大器）
（1）、 Integrating amplifier
（2）、 Differentiating amplifier
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Current-voltage conversion （电流—电压转换器）
（1） Current to-voltage
（2）
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References
1、P. Horowitz and W. Hill, 1989, The Art of Electronics, 2nd Ed.,
Cambridge University Press, Cambridge, UK
2、D. C. Ramsay, 1996, Principles of Engineering Instrumentation,
Arnold, London, UK
3、F. F. Mazda, 1987, Electronic instruments and measurement
techniques, Cambridge Univ. Pr., New York
4、A. J. Diefenderfer, 1972, Principles of electronic instrumentation,
W. B. Sanuders Co., Philadelphia, PA.
5、R. Pallas-Areny and J. G. Webster, 1991, Sensors and Signal
Conditioning, Wiley, New York
6、J. W. Gardner, 1994, Microsensors. Principles and Applications,
Wiley, New York.
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