GT4518 AC Bridge Principle and Design Laboratory Instrument Manual
Principle and design of AC bridge
AC bridge is a kind of comparative instrument, which plays an important role in electrical measurement technology. It is mainly used to measure AC equivalent resistance and its time constant; capacitance and dielectric loss; self-inductance and its coil quality factor and mutual inductance. Precision measurement, can also be used for non-electrical conversion to the precise measurement of the corresponding power parameters.
Commonly used AC bridges are divided into impedance ratio bridges and transformer bridges. It is customary to refer to the impedance ratio bridge as an AC bridge. In this experiment, the AC bridge refers to the impedance ratio of the bridge. The line of the AC bridge and DC A single bridge circuit has the same structure, but because its four arms are impedance, its balance conditions, line composition, and balance adjustment are achieved.
The process is more complicated than the DC bridge.
ã€Purpose】
1. Master the balance conditions and measurement principle of the AC bridge
2. Design various AC bridges for actual measurement
3. Verify the balance conditions of the AC bridge
[Principle of AC Bridge]
Figure 1 is the principle circuit of an AC bridge. It is similar to the principle of a DC single bridge. In an AC bridge, the four bridge arms are generally composed of AC circuit components such as resistors, inductors, and capacitors; the power supply of the bridge is usually a sinusoidal AC power supply. ; There are many types of AC balance indicators, suitable for
Figure 1 AC bridge principle
In different frequency ranges, the resonant galvanometer can be used when the frequency is below 200Hz; the earphone can be used as the balance indicator in the audio range; the electronic zero-pointing instrument can also be used in the audio or higher frequency; also use the electronic oscilloscope or communication The millivoltmeter is used as a balance indicator. This experiment uses a high-sensitivity electronically amplified zero-pointer with sufficient sensitivity. When the indicator points to zero, the bridge reaches equilibrium.
First, the balance condition of the AC bridge
We discuss the basic principle of an AC bridge under sinusoidal steady state conditions. In an AC bridge, the four bridge arms are composed of impedance elements, and an AC zero gauge is connected to one diagonal cd of the bridge, and the other diagonal Connect the AC power to the line ab.
When the bridge parameters are adjusted so that no current flows through the AC zero meter (ie, I0 = 0), the potentials of the two points of cd are equal, and the bridge reaches equilibrium. At this time, Uac=Uad Ucb=Udb
I1Z1=I4Z4 I2Z2=I3Z3
When the bridge is balanced, I0=0, from which I1=I2, I3=I4, so Z1Z3=Z2Z4 (1)
The above formula is the equilibrium condition of the AC bridge. It shows that when the AC bridge reaches equilibrium, the product of the impedance of the bridge arm is equal.
It can be seen from Fig. 1 that if the first bridge arm is composed of the measured impedance Zx, then Zx= Z4
When the parameters of other bridge arms are known, the value of the measured impedance Zx can be determined.
Second, the analysis of the balance of the AC bridge
Below we will further analyze the balance conditions of the bridge.
In the case of sinusoidal AC, the bridge arm impedance can be written in the form of a complex number Z=R+jX=Zejφ. If the equilibrium condition of the bridge is expressed in the form of a complex number, then it can be obtained.
Z1ejφ1·Z3ejφ3=Z2ejφ2·Z4ejφ4 ie Z1·Z3 ej(φ1+φ3)=Z2·Z3 ej(φ2+φ4)
According to the condition that the complex numbers are equal, the amplitude and the amplitude of the two ends of the equation must be equal, so
Z1Z3=Z2Z4
Φ1+φ3=φ2+φ4
The above is another manifestation of the equilibrium condition. It can be seen that the balance of the AC bridge must satisfy two conditions: one is that the product of the impedance amplitude modes on the opposite bridge arms is equal; the other is that the sum of the impedance angles on the opposite bridge arms is equal.
From the formula (2), the following two important conclusions can be drawn.
1. The AC bridge must be configured with the impedance of the bridge arm in a certain way.
If four bridges of any different nature are used to form a bridge, it is not always possible to adjust to the balance. Therefore, the properties of the components of the bridge must be properly matched according to the two equilibrium conditions of the bridge.
In many AC bridges, in order to make the bridge structure simple and easy to adjust, the two bridge arms in the AC bridge are usually designed as pure resistors.
From the equilibrium condition of equation (2), if the adjacent two arms are connected to the pure resistance, the adjacent two arms must also access the impedance of the same nature. For example, if the object Zx is in the first bridge arm, the two phases If the adjacent arms Z2 and Z3 (Fig. 1) are pure resistors, that is, φ2=φ3=0, then the equation (2) can be obtained: φ4=φx. If the object to be measured Zx is a capacitor, then its adjacent bridge arm Z4 is also Must be a capacitor; if Zx is an inductor, Z4 must also be an inductor.
If the pure armature is connected to the bridge arm, the other two bridge arms must be opposite-resistance. For example, if the bridge arms Z2 and Z4 are pure resistors, that is, φ2=φ4=0, then the equation (2) can be known: φ3= -φx; If the object Zx is a capacitor, its opposite arm Z3 must be an inductor, and if Zx is an inductor, Z3 must be a capacitor.
2, AC bridge balance must repeatedly adjust the parameters of the two bridge arms
In the AC bridge, in order to meet the above two conditions, the parameters of the two bridge arms must be adjusted in order to fully balance the bridge, and the two parameters are often adjusted repeatedly, so the balance adjustment of the AC bridge is better than The adjustment of the DC bridge is more difficult.
[Design of AC Bridge]
This experiment uses independent measuring components, which can not only design a theoretically balanced bridge type, but also design a theoretically unbalanced bridge type to verify the working principle of the AC bridge.
According to the previous analysis, the four bridge arms of the AC bridge can be balanced according to certain principles. According to the previous analysis, there are many types of bridge arms that meet the equilibrium conditions. Design a good and practical AC bridges should pay attention to the following aspects:
(1) The bridge arm should not use the standard inductor as much as possible. Due to the manufacturing process, the accuracy of the standard capacitor is higher than that of the standard inductor, and the standard capacitor is not easily affected by the external magnetic field. Therefore, the commonly used AC bridge, whether it is the inductance and Measuring capacitance, except for the arm to be measured, the other three arms use capacitors and resistors.
(2) Try to make the balance condition independent of the power frequency, so that the advantages of the bridge can be exerted, so that the measurement is only determined by the bridge arm parameters, and is not affected by the voltage or frequency of the power supply. Some forms of bridge balance conditions and Frequency is related, so that the frequency of the power supply will directly affect the accuracy of the measurement.
(3) The bridge needs to be adjusted repeatedly in the balance, so that the relationship between the amplitude angle and the amplitude mode can be satisfied at the same time. Usually, the degree of the bridge tending to balance is called the convergence of the AC bridge. The better the convergence, the bridge The faster the trend is balanced; the convergence is poor, the bridge is not easy to balance or the balancing process takes a long time, and the time required for measurement is also long. The convergence of the bridge depends on the nature of the bridge arm impedance and the choice of adjustment parameters. Poor bridges are not commonly used because of the difficulty of balance.
Of course, for the needs of theoretical verification, we can also form the various forms of AC bridges that we need.
Below are several commonly used AC bridges.
First, the capacitor bridge
Capacitor bridge is mainly used to measure the capacitance and loss angle of the capacitor. In order to understand the working condition of the capacitor bridge, first analyze the equivalent circuit of the capacitor under test, and then introduce the typical circuit of the capacitor bridge.
1. The equivalent circuit of the measured capacitor
The actual capacitor is not an ideal component, it has dielectric loss, so the phase difference between the current through the capacitor C and the voltage across it is not 90°, and a δ angle smaller than 90° is called the dielectric loss angle. The capacitor can be represented by two forms of equivalent circuits. One is an equivalent circuit in which an ideal capacitor and a resistor are connected in series, as shown in Figure 2a. One is an equivalent circuit in which an ideal capacitor is connected in parallel with a resistor. As shown in Fig. 3a, in the equivalent circuit, the ideal capacitance represents the equivalent capacitance of the actual capacitor, and the series (or parallel) equivalent resistance represents the heating loss of the actual capacitor.
Figure 2 (a) series equivalent circuit diagram of lossy capacitor
Figure 2 (b) vector
Figure 2b and Figure 3b respectively show the phasor diagram of the corresponding voltage and current. It must be noted that C and R in the equivalent series circuit are not equal to Cˊ and Rˊ in the equivalent parallel circuit. In general, When the dielectric loss of the capacitor is not large, there should be C≈Cˊ, R≤Rˊ. Therefore, if R or R ˊ is used to represent the loss of the actual capacitor, it must also be stated which equivalent circuit it is used for. Therefore, for convenience of presentation, the medium is usually represented by the tangent tg δ of the loss angle δ of the capacitor. Loss characteristic, and is represented by the symbol D, which is usually called the loss factor in the equivalent series circuit.
D=tgδ= ==ωCR
Figure 3 (a) Parallel equivalent circuit of lossy capacitor
Figure 3 (b) vector
In an equivalent parallel circuit
D=tgδ= ==
It should be noted that in Fig. 2b and Fig. 3b, δ=90°-φ is suitable for both equivalent circuits, so the loss factor obtained is consistent regardless of which equivalent circuit is used.
2. Capacitance bridge with small loss measurement (series resistance type)
Figure 4 is a capacitor bridge suitable for measuring the measured capacitance with low loss. The measured capacitance Cx is connected to the first arm of the bridge, equivalent to the capacitor Cx' and the series resistor Rx', where Rx' represents its loss. The standard capacitor Cn compared with the measured capacitor is connected to the adjacent fourth arm, and a variable resistor Rn is connected in series with Cn. The other two arms of the bridge are pure resistors Rb and Ra. When the bridge is adjusted to balance, Have
(Rx+ )Ra=(Rn+ )Rb makes the real part and the imaginary part of the above formula equal
RxRa=RnRb
=
Last seen
Rx=
Rn (3)
Cx= Cn (4)
It can be seen that in order to balance the bridge, the above two conditions must be met at the same time, so at least two parameters can be adjusted. If Rn and Cn are changed, the capacitor bridge can be balanced independently without affecting each other. The standard capacitor is usually used. They are all fixed, so Cn can't be connected. In this case, we can adjust the Ra/Rb ratio to make equation (4) satisfied, but adjust the Ra/Rb ratio to affect the balance of equation (3). In order to make the bridge meet the two balance conditions at the same time, it is necessary to repeatedly adjust the parameters such as Rn and Ra/Rb. Therefore, when using the AC bridge, it is necessary to gain experience through actual operation, and the bridge balance can be quickly obtained. The bridge is balanced. After that, the Cx and Rx values ​​can be calculated according to equations (3) and (4), respectively, and the loss factor D of the measured capacitor is
D=tgδ=ωCxRx=ωCnRn (5)
Figure 4 Series Resistive Capacitor Bridge
Figure 5 Parallel Resistive Capacitor Bridge
3. Capacitance bridge with large loss measurement (parallel resistance type)
If the loss of the measured capacitor is large, the resistance Rn connected in series with the standard capacitor must be large when measuring with the above bridge, which will reduce the sensitivity of the bridge. Therefore, when the loss of the measured capacitor is large, the map should be used. The circuit of another capacitor bridge shown in 5 is used for measurement. It is characterized in that the standard capacitor Cn and the resistor Rx are connected in parallel with each other, and can be written according to the balance condition of the bridge.
Rb[ 〕=Ra[ 〕
Available after finishing
Cx=Cn (6)
Rx=Rn (7)
And the loss factor is
D=tgδ= = (8)
The AC bridge measures capacitance as needed. There are other forms as well. See also related book design.
Second, the inductor bridge
The inductor bridge is used to measure the inductance. The inductor bridge has a variety of lines. The standard capacitor is usually used as the standard component compared with the measured inductor. From the previous analysis, the standard capacitor must be placed and tested. Inductance relative to the bridge arm. According to the actual needs, standard inductor can also be used as the standard component. At this time, the standard inductor must be placed in the bridge arm adjacent to the measured inductor, which will not be introduced here.
Generally, the actual inductor coil is not a pure inductor. In addition to the reactance XL=ωL, there is also an effective resistor R. The ratio of the two is called the quality factor of the inductor coil Q. That is, Q=
The following two inductor bridge circuits are suitable for measuring high Q and low Q inductor components.
1. Measure the inductance bridge of high Q inductor
The principle circuit of the inductor bridge measuring high Q value is shown in Figure 6, which is also called Hai's bridge.
When the bridge is balanced, it can be obtained according to the balance condition.
(RX+jωLX)[Rn+ ]=RbRa
Simplified and organized
LX=
RX=
It can be known from equation (9) that the balance condition of the Hai's bridge is related to the frequency. Therefore, when applying the finished bridge, if the external power supply is used instead, the frequency of the power supply must be the same as the power frequency specified in the bridge manual. Correspondence, and the power waveform must be a sine wave, otherwise, the harmonic frequency will affect the accuracy of the measurement.
When measured with a Hai's bridge, its Q value is
Q= =
(10)
It can be known from equation (10) that the smaller the Q value of the measured inductor is, the larger the value of the standard capacitor Cn is required, but the capacity of the standard capacitor cannot be made too large. In addition, if the Q value of the measured inductor is too small, Haishidian
The Rn of the bridge in the standard capacitor of the bridge must also be large, but when the impedance value of one of the bridge arms is too large, it will affect the sensitivity of the bridge. It can be seen that the Haishi bridge line is suitable for measurement. The Q value is larger for the inductance parameter, and when measuring the parameter of the inductance component with Q<10, another bridge circuit is needed. The following describes the bridge circuit suitable for measuring the low Q inductance.
Figure 6 Bridge principle for measuring high Q inductors
Figure 7 Bridge principle for measuring low Q inductors
2. Measure the inductance bridge of low Q inductor
The bridge principle circuit for measuring low Q inductors is shown in Figure 7. This bridge circuit is also known as the Maxwell bridge. This bridge is different from the bridge circuit for measuring high Q inductors described above: Standard The Cn. and the variable resistor Rn in the bridge arm of the capacitor are connected in parallel.
When the bridge is balanced, there is
(RX+jωLX)[ ]=RbRa The corresponding measurement result is
LX=RbRaCn
Rx= Ra
The quality factor Q of the measured object is Q= =ωRnCn (12)
The balance condition of the Maxwell bridge (11) shows that its balance is frequency-independent, that is, the bridge can be balanced if the power supply is any frequency or non-sinusoidal, and the actual measurable Q range is also Larger, so the application range of the bridge is wider. But in fact, due to the mutual influence between the components in the bridge, the measurement frequency of the AC bridge still has a certain influence on the measurement accuracy.
Third, the resistance bridge
The Wheatstone bridge is used to measure the resistance. See Figure 8. The visible bridge form is the same as the DC single-arm bridge, except that AC power and AC zero-meter are used as measurement signals.
When the galvanometer G is balanced, no current flows through G, and two points of cd are equipotential, then: I1 = I2, I3 = I4
The following formula holds: I1R1=I4R4 I2R2 =I3R3- Then there is
= So RX=
·R2 is RX=
·Rb
Since AC power and AC resistance are used as the bridge arms, it is difficult to balance when measuring some resistors with large residual reactance. In this case, DC bridge can be used for measurement.
ã€laboratory apparatus】
GT4518 AC Bridge Tester
[Experimental content]
Before the experiment, the experimental principle should be fully grasped, and the corresponding bridge circuit should be designed. The wrong bridge may have large measurement error or even measurement.
Due to the modular design, the connection of the experiment is more. Pay attention to the correctness of the wiring, which can shorten the experiment time; use the instrument civilized, use the special connection line correctly, do not pull the lead part, do not beat each time when balancing Components, but should find the reason. This can improve the life of the instrument.
The AC bridge uses an AC zero meter, so the pointer is located on the left side of the 0 position when the bridge is balanced.
Figure 8 AC bridge measuring resistor
During the experiment, the sensitivity of the zero gauge should be adjusted to the appropriate position first, and the pointer position is at 30-80% of the full scale. When the basic balance is reached, the sensitivity is adjusted again, and the bridge is re-adjusted until the final balance.
1, AC bridge measurement capacitance
2, AC bridge measurement inductance
3, AC bridge measuring resistance
4, the design of other bridges
Wayfinding Sign,Wayfinding Signage,Curved Sign Holder,Outdoor Advertising Signage
Chengdu GodShape Sign Co., Ltd , https://www.signsgs.com