{"id":37,"date":"2018-11-28T05:25:27","date_gmt":"2018-11-28T05:25:27","guid":{"rendered":"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=37"},"modified":"2019-05-01T04:31:58","modified_gmt":"2019-05-01T04:31:58","slug":"bridges-controlled-circuits-ii","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/chapter\/bridges-controlled-circuits-ii\/","title":{"rendered":"Bridges Controlled Circuits – II"},"content":{"raw":"
\"epgp<\/a>\r\n<\/span><\/div>\r\n
\r\n\r\n\u00a0 \u00a0 Learning Ojectives<\/span><\/strong>\r\n\r\nIn this module we will study about AC bridge circuits.\r\n\r\n \r\n\r\n1.\u00a0First we will look into classification of AC bridges in the introduction.\r\n\r\n \r\n\r\n2. Under AC Bridges will study about capacitance comparison bridge and its variant Wein Bridge\r\n\r\n \r\n\r\n3. And then we will study about Inductance Comparison Bridge and Resonance Bridge Circuit\r\n\r\n \r\n\r\nIntroduction<\/strong><\/span>\r\n\r\n \r\n

In previous module, we looked into DC bridges, now we will study AC bridges. AC bridges cannot only be used for measuring resistance but also inductance and capacitance. The unknown quantities whether resistor, capacitor or inductor may be be attached in series or in parallel in one of the arms of the bridge. Over working and principle of operation behind the AC bridges is similar to Wheatstone. In LCR bridge circuit, i.e. resonance bridge three electrical components, resistor, capacitor or inductor are in series. Whereas, in other types of AC bridges one may have 2 components in series or in parallel.<\/p>\r\n \r\n

A. C. Bridges can be broadly classified into Capacitance Comparison Bridge and Inductance Comparison Bridge. Both Wein and Resonance Bridge circuits measure unknown quantities via combination of capacitor, inductor or resistor either in parallel or in series in one of the arms of the bridge circuit. Here our objectives are same, that two balance 2 arms of the bridges and potential drop is measured by a null detector i.e. galvanometer.<\/p>\r\n \r\n\r\nA.C. Bridges<\/strong><\/span>\r\n\r\n \r\n\r\nLet us first look at capacitance comparison bridge.\r\n\r\n \r\n\r\nCapacitance Comparison Bridge.<\/strong>\r\n\r\n \r\n

In order to best understand Capacitance bridge, it is important to understand bridge balance equation. As shown in figure 1(a), potential at point C & D should be equal in\u00a0terms of amplitude and phase. Therefore for a balanced bridge, <\/span>potential drop from point A to C should be equal to A to D. <\/span>These potential can <\/span>written as<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\nEac<\/sub> = Ead<\/sub> ------(1)\r\n\r\nAccording to ohms law potentials can be written as\r\n\r\nI1<\/sub>.Z1<\/sub> = I2<\/sub>.Z2<\/sub> ------- (2)\r\n\r\nWhere I is the current and Z is the impedance of capacitor or inductor\r\n\r\nWhen no current flows through the null detector-\r\n\r\nI3<\/sub> = I1<\/sub> & I4<\/sub> = I2<\/sub>\r\n\r\n \r\n\r\n\"\"\r\n\r\nby substituting equation 3 & 4 into equation 2 and solving both sides we get balanced equation of impedance for the magnitudes \u2013\r\n\r\nZ1<\/sub>.Z4<\/sub> = Z2<\/sub>. Z3<\/sub> ------ (5)\r\n\r\n \r\n\r\n\"\"\r\n\r\n \r\n\r\nFigure 1. <\/strong>(a) A standard bridge for balance equation. (b) Capacitance comparison bridge.\r\n\r\n \r\n

From the balanced equation one can derive equation for measuring unknown capacitance Cx<\/sub> and resistance Rx<\/sub>. Here, R3<\/sub> is the variable resistor to balance the bridge and C3<\/sub> is the standard capacitor in series with R3<\/sub>. The unknown capacitor is\u00a0compared with the standard capacitor and under balanced <\/span>conditions the capacitor and its leakage resistance value are measured. The net impedance at <\/span>the each arm of the bridge is given by<\/span><\/p>\r\n \r\n

Z1<\/sub> = R1<\/sub> + j0 \uf057 ------- (6)<\/span><\/p>\r\n

Z2<\/sub> = R2<\/sub> + j0 \uf057 -------- (7)<\/span><\/p>\r\n \r\n

Here, Z1 and Z2 are resistors whose capacitive reactance is zero.<\/span><\/p>\r\n

Z3<\/sub> = R3<\/sub> \u2013 j.XC3<\/sub> = R3<\/sub> \u2013 j ( 1\/ w.C3<\/sub>) \uf057 ------- (8)<\/span><\/p>\r\n

Z4<\/sub> = Rx<\/sub> \u2013 j.XCx<\/sub> = Rx<\/sub> - j ( 1\/ w.Cx<\/sub>) \uf057 -------- (9)<\/span><\/p>\r\n \r\n

Substituting the above values into the balanced equation,<\/span><\/p>\r\n

Z1.Z4<\/sub> = Z2<\/sub>. Z3<\/sub><\/span><\/p>\r\n \r\n

We get,<\/span><\/p>\r\n

R1.<\/sub>Rx<\/sub> \u2013 j.(R1<\/sub>\/ w.Cx<\/sub>) = R2<\/sub>.R3<\/sub> \u2013 j.( R2<\/sub>\/ w.C3<\/sub>) ---- (10)<\/span><\/p>\r\n \r\n

On equating the real parts, we get<\/span><\/p>\r\n

R1<\/sub>. Rx<\/sub> = R2<\/sub>.R3<\/sub> -------- (11)<\/span><\/p>\r\n

Rx<\/sub> = (R2<\/sub>.R3<\/sub>)\/ R1<\/sub> -------(12)<\/span><\/p>\r\n \r\n

On equating the imaginary parts<\/span><\/p>\r\n

R1<\/sub>\/(w.Cx<\/sub>) = R2<\/sub>\/(w.C3<\/sub>) ------ (13)<\/span><\/p>\r\n \r\n

Cx<\/sub> =(C3<\/sub>.R1<\/sub>)\/R1<\/sub> ------ (14)<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n

Therefore from equations 12 & 14 one can determine the value of unknown capacitor and its leakage resistance. Experimentally true balance can be obtained by varying R1 and R3 simultaneously.<\/p>\r\n \r\n\r\nAnother type of AC bridge is\r\n\r\n \r\n\r\nWein Bridge<\/strong>\r\n\r\n \r\n

A variant of Capacitance Bridge is <\/span>Wein Bridge,<\/em> which has 4 resistors and two capacitors. It is important to note this bridge does not require equal values of R & C. In one arm we have RC combination in series and in the adjacent arm its\u2019 in a parallel combination. This bridge is designed to measure frequency and is used for measuring unknown capacitor with great accuracy. The arm in which capacitor is in parallel to variable resistor R3, admittance value is used rather than impedance.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n

Figure 2. <\/strong>Circuit Diagram of Wein Bridge. It has two variable resistors R1 <\/sub>and R3<\/sub> and two fixed resistor R2<\/sub> & R4<\/sub>. Capacitor C3<\/sub> is parallel to R3<\/sub> and Capacitor C1<\/sub> is in series with R1<\/sub>.<\/p>\r\n \r\n\r\n \r\n\r\nAdmittance for the arm is written as \u2013\r\n\r\n \r\n\r\nY3<\/sub> = 1\/R3<\/sub> + j.w.C3<\/sub> ---------- (15)<\/span>\r\n\r\n \r\n\r\nIn the balance equation Z3 is replaced by 1\/Y3<\/sub>\r\n\r\nTherefore balance equation can be written as \u2013\r\n\r\n \r\n\r\nZ1<\/sub>. Z4<\/sub> = Z2<\/sub>\/Y3<\/sub>, i.e. Z2<\/sub> = Z1<\/sub>. Z4<\/sub>.Y3<\/sub>\r\n\r\n \r\n\r\nOn substituting and rearranging the terms we get \u2013\r\n\r\n \r\n\r\n\"\"\u00a0 \u00a0By equating real and imaginary terms we get \u2013\r\n\r\n<\/div>\r\n\"\"\r\n

\r\n\r\n \r\n

The bridge can be used for measuring frequency within the audio range. Here R1 & R3 are kept at identical values and capacitors are normally of fixed values.<\/p>\r\n \r\n

There are two conditions under which bridge is balanced, i.e. equation 18 determines the required resistance ratio R1\/R4 and equation 20 is used to determine frequency of the applied voltage. This means if we balance the resistance ratio in equation 18 and simultaneously excite the bridge at a frequency given in equation 20, the bridge will get balanced.<\/p>\r\n \r\n

For a Wein bridge, circuits components are chosen such that R1<\/sub> = R3<\/sub> =R and C1<\/sub> = C2<\/sub>= C. For equation 18, it reduces ratio R1<\/sub>\/R2<\/sub> =2 and frequency equation 20 to f= 1\/2 RC<\/em>. The bridge can measure frequencies within the audio range. The frequencies with the audio range are divided into 20-200, 200-2000, 2000-20kHz ranges. Here, resistances are modulated to change the frequency range and further fine control within the range\u00a0is obtained by adjusting capacitors C1<\/sub> &C2<\/sub>. If one desires to measure capacitances, in that <\/span>case frequency of operation of the AC Source should be known.<\/span><\/p>\r\n \r\n

The bridge can also be used as Harmonic distortion analyzer or as a Notch Filter. The bridge is used as <\/span>frequency determining element in audio and radio frequency oscillators. With Wein Bridge, <\/span>accuracy of 0.5%-1% can be readily obtained but since the bridge is frequency sensitive, it is difficult to obtained balance unless the applied voltage waveform is purely sinusoidal.<\/span><\/p>\r\n \r\n

Now we will study about<\/span>..<\/p>\r\n \r\n

Inductance Comparison Bridge<\/strong><\/p>\r\n \r\n

Inductance Comparison Bridge is similar to Capacitance Comparison Bridge, <\/span>only difference being the replacement of capacitors with inductors. This bridge is used for measuring unknown inductance Lx<\/sub> and its internal resistance Rx<\/sub>. It has two pure resistances R1<\/sub> & R2<\/sub>, a variable resistor R3<\/sub> with inductor L3<\/sub> and an unknown inductor Lx<\/sub> having an internal resistance Rx.<\/span><\/p>\r\n \r\n

As discussed for capacitance, the impedance for an inductor can be written as -<\/span><\/p>\r\n \r\n

Z = R + j(w.L) \uf057 --------- (21)<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n

Figure 3<\/strong>. Circuit diagram for Inductance Comparison Bridge On substituting equation 21 into the balanced impedance equation 5 we get -<\/p>\r\n \r\n

R1<\/sub>.Rx<\/sub> + j .w.R1<\/sub>.Lx = R2<\/sub>.R3<\/sub> - j .w.R2<\/sub>.L3<\/sub> ---- (22)<\/p>\r\n \r\n

On equating the real parts we get \u2013<\/p>\r\n \r\n\r\nRx<\/sub> = (R2<\/sub>.R3<\/sub>)\/R1<\/sub>\u00a0 -------- (23)\r\n\r\n \r\n\r\nOn equating the imaginary parts we get \u2013\r\n\r\n \r\n\r\nLx<\/sub> = (R2<\/sub>. L3<\/sub>)\/R1<\/sub> --------- (24)<\/span>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n

To the balance the bridge, inductive balance control is achieved by R2<\/sub> and resistance balance control is achieved by R3<\/sub>. By alternatingly varying the L3<\/sub> or R3<\/sub> the balance for the inductance comparison bridge is obtained<\/p>\r\n \r\n

Resonance Bridge<\/strong><\/p>\r\n\"\"\r\n\r\n \r\n

Figure. 4. <\/strong>\u2013 Circuit diagram for Resonance Bridge<\/p>\r\n \r\n

A resonance bridge is a third category of bridge that contains a resistor (Rx<\/sub>), capacitor (Cx<\/sub>) and an inductor (Lx<\/sub>) in series in one of its arms. Other three arms consist of resistor only. On substituting values to bridge balance equation we get \u2013<\/p>\r\n \r\n

R1<\/sub>. (Rx<\/sub> +j.w.Lx \u2013 j\/(jCx)) = R2.R3 ---- (30)<\/p>\r\n \r\n\r\nOn equating real terms we get \u2013\r\n\r\n \r\n\r\nRx = (R2.R3)\/R1 --------(31)<\/span>\r\n\r\n \r\n\r\nOn equating imaginary terms we get \u2013<\/span>\r\n\r\n \r\n\r\nj.w.Lx \u2013 j\/(w.Cx) = 0<\/span>\r\n\r\n \r\n\r\nw2<\/sup>= 1\/(Lx.Cx) ---------- (32)<\/span>\r\n\r\n<\/div>\r\nResonant frequency of this series resonance circuit can be calculated with the following equation \u2013<\/span>\r\n\r\n \r\n

\r\n\r\n\"\"\r\n\r\nFor measuring unknown inductor, a standard capacitor is varied until balance is obtained then \u2013\r\n\r\n \r\n\r\nLx = 1\/(w2<\/sup>. Cx) ----------- (34)<\/span>\r\n\r\n \r\n\r\nFor measuring unknown capacitor, a standard inductance is varied until balance is obtained then \u2013\r\n\r\n \r\n\r\nCx = 1\/(w2<\/sup>. Lx) -------------- (35)<\/span>\r\n\r\n \r\n

It is important to note that operating frequency of the generator should be known in order to find out an unknown quantity.<\/p>\r\n \r\n

Digital Readout Bridge<\/strong><\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n

Figure 5. <\/strong>Block diagram of Wheatstone Bridge with Digital Readout<\/p>\r\n \r\n

With advent of digital circuitry there is tremendous effect on electronic testing instruments. Use of digital circuits has helped in developing Digital Readout Bridge.\u00a0Bridge\u2019s configuration i.e. actual measuring circuitry hasn\u2019t <\/span>change much and this system has also removed operator error while observing the reading. The diagram shown in figure 5 is of a Wheatstone bridge with a digital readout circuit. From the diagram one can observe that a logic circuit provides a signal to R3, it senses the null and provides a representing value for Rx.<\/span><\/p>\r\n \r\n

There are different\u2026.<\/span><\/p>\r\n \r\n

Types of Detectors, <\/strong>- based on their application and frequency range is given below\u2026<\/span><\/p>\r\n\r\n

    \r\n \t
  1. At low frequency, <\/span>best detector is vibrational galvanometer.<\/span><\/li>\r\n \t
  2. For laboratory work and frequencies upto 100 Hz, moving coil type is the most preferred <\/span>due its high sensitivity.<\/span><\/li>\r\n \t
  3. For frequencies between 300 Hz- 1 kHz, and for high voltages, moving magnet type vibrational galvanometer with remote controlled tuning are preferred.<\/span><\/li>\r\n \t
  4. For audio frequencies greater than 800 Hz, headphones are best detector. It is important to note that vibrational galvanometers and headphones do not have phase sensitivity. That means they cannot indicate whether resistance or reactance adjustment is required.<\/span><\/li>\r\n \t
  5. At low frequencies and for high sensitivity, ac galvanometer and separately excited dynamometer having phase sensitivity are best suited.<\/span><\/li>\r\n \t
  6. For routine measurement of bridges, pointer instruments are used. It is more advantageous if such instruments are made phase selective. Predominantly Pointer instruments are moving coil milliammeters and are operated via some arrangement of copper oxide rectifiers. And have a working range of (40 Hz-1 kHz)<\/li>\r\n \t
  7. Modern bridges are regularly fitted with an amplifier<\/li>\r\n \t
  8. A heterodyne or beat-tone detector are used for high audio or radio frequencies, or frequencies above 3 kHz<\/li>\r\n \t
  9. For almost all bridges, impedance should be selected that best suits the bridge. An Interbridge transformer can help in obtaining higher sensitivity. When using a headphone as a detector, one must take precaution to eliminate any capacitance effects between the observer and the headphones.<\/span><\/li>\r\n \t
  10. The range of moving magnet vibration galvanometer is up to 1500 Hz.<\/li>\r\n \t
  11. As an ac detector, an electrodynamometer can also be used.<\/li>\r\n \t
  12. Small capacitances have very large impedance, especially in an ac circuit at low frequency and when measured in a bridge they tend to form a high impedance branch. Hence, electrometer is used as a detector to increase sensitivity.<\/li>\r\n<\/ol>\r\n<\/div>\r\n\u00a0 \u00a0 Summary<\/strong>\r\n\r\nIn this module we studied about AC bridge circuits.\r\n
      \r\n \t
    1. First we looked into classification of AC bridges in the introduction.<\/li>\r\n \t
    2. Under AC Bridges we studied about capacitance comparison bridge and its variant Wein Bridge<\/li>\r\n \t
    3. And then we studied about Inductance Comparison Bridge and Resonance Bridge Circuit<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n
      you can view video on Bridges Controlled Circuits - II<\/strong><\/td>\r\n\"\"<\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\u00a0 \u00a0\u00a0References :-<\/strong>\r\n
        \r\n \t
      1. Electrical and Electronic Measurements and Instrumentation, Sawhney A. K.<\/em>, Dhanpat Rai & Sons, Reprint 1985<\/li>\r\n \t
      2. Measurements and Instrumentation, Bakshi U.A., Bakshi A.V.,<\/em> Technical Publications, 2009<\/li>\r\n \t
      3. Principles of instrumental analysis, Skoog, Douglas A., F. James Holler, and<\/em> Stanley R. Crouc,. <\/em>Cengage learning, Edition 2017<\/li>\r\n \t
      4. Instrumentation, measurement and analysis. Nakra, B.C. and Chaudhry, K.K.,<\/em> Tata McGraw-Hill Education, 2003.<\/li>\r\n \t
      5. Measurement and instrumentation: theory and application, Morris, A. S., &<\/em> Langari, R<\/em>. , Academic Press, 2012.<\/li>\r\n<\/ol>","rendered":"
        \"epgp<\/a>
        \n<\/span><\/div>\n
        \n

        \u00a0 \u00a0 Learning Ojectives<\/span><\/strong><\/p>\n

        In this module we will study about AC bridge circuits.<\/p>\n

         <\/p>\n

        1.\u00a0First we will look into classification of AC bridges in the introduction.<\/p>\n

         <\/p>\n

        2. Under AC Bridges will study about capacitance comparison bridge and its variant Wein Bridge<\/p>\n

         <\/p>\n

        3. And then we will study about Inductance Comparison Bridge and Resonance Bridge Circuit<\/p>\n

         <\/p>\n

        Introduction<\/strong><\/span><\/p>\n

         <\/p>\n

        In previous module, we looked into DC bridges, now we will study AC bridges. AC bridges cannot only be used for measuring resistance but also inductance and capacitance. The unknown quantities whether resistor, capacitor or inductor may be be attached in series or in parallel in one of the arms of the bridge. Over working and principle of operation behind the AC bridges is similar to Wheatstone. In LCR bridge circuit, i.e. resonance bridge three electrical components, resistor, capacitor or inductor are in series. Whereas, in other types of AC bridges one may have 2 components in series or in parallel.<\/p>\n

         <\/p>\n

        A. C. Bridges can be broadly classified into Capacitance Comparison Bridge and Inductance Comparison Bridge. Both Wein and Resonance Bridge circuits measure unknown quantities via combination of capacitor, inductor or resistor either in parallel or in series in one of the arms of the bridge circuit. Here our objectives are same, that two balance 2 arms of the bridges and potential drop is measured by a null detector i.e. galvanometer.<\/p>\n

         <\/p>\n

        A.C. Bridges<\/strong><\/span><\/p>\n

         <\/p>\n

        Let us first look at capacitance comparison bridge.<\/p>\n

         <\/p>\n

        Capacitance Comparison Bridge.<\/strong><\/p>\n

         <\/p>\n

        In order to best understand Capacitance bridge, it is important to understand bridge balance equation. As shown in figure 1(a), potential at point C & D should be equal in\u00a0terms of amplitude and phase. Therefore for a balanced bridge, <\/span>potential drop from point A to C should be equal to A to D. <\/span>These potential can <\/span>written as<\/span><\/p>\n<\/div>\n

        \n

        Eac<\/sub> = Ead<\/sub> ——(1)<\/p>\n

        According to ohms law potentials can be written as<\/p>\n

        I1<\/sub>.Z1<\/sub> = I2<\/sub>.Z2<\/sub> ——- (2)<\/p>\n

        Where I is the current and Z is the impedance of capacitor or inductor<\/p>\n

        When no current flows through the null detector-<\/p>\n

        I3<\/sub> = I1<\/sub> & I4<\/sub> = I2<\/sub><\/p>\n

         <\/p>\n

        \"\"<\/p>\n

        by substituting equation 3 & 4 into equation 2 and solving both sides we get balanced equation of impedance for the magnitudes \u2013<\/p>\n

        Z1<\/sub>.Z4<\/sub> = Z2<\/sub>. Z3<\/sub> —— (5)<\/p>\n

         <\/p>\n

        \"\"<\/p>\n

         <\/p>\n

        Figure 1. <\/strong>(a) A standard bridge for balance equation. (b) Capacitance comparison bridge.<\/p>\n

         <\/p>\n

        From the balanced equation one can derive equation for measuring unknown capacitance Cx<\/sub> and resistance Rx<\/sub>. Here, R3<\/sub> is the variable resistor to balance the bridge and C3<\/sub> is the standard capacitor in series with R3<\/sub>. The unknown capacitor is\u00a0compared with the standard capacitor and under balanced <\/span>conditions the capacitor and its leakage resistance value are measured. The net impedance at <\/span>the each arm of the bridge is given by<\/span><\/p>\n

         <\/p>\n

        Z1<\/sub> = R1<\/sub> + j0 \uf057 ——- (6)<\/span><\/p>\n

        Z2<\/sub> = R2<\/sub> + j0 \uf057 ——– (7)<\/span><\/p>\n

         <\/p>\n

        Here, Z1 and Z2 are resistors whose capacitive reactance is zero.<\/span><\/p>\n

        Z3<\/sub> = R3<\/sub> \u2013 j.XC3<\/sub> = R3<\/sub> \u2013 j ( 1\/ w.C3<\/sub>) \uf057 ——- (8)<\/span><\/p>\n

        Z4<\/sub> = Rx<\/sub> \u2013 j.XCx<\/sub> = Rx<\/sub> – j ( 1\/ w.Cx<\/sub>) \uf057 ——– (9)<\/span><\/p>\n

         <\/p>\n

        Substituting the above values into the balanced equation,<\/span><\/p>\n

        Z1.Z4<\/sub> = Z2<\/sub>. Z3<\/sub><\/span><\/p>\n

         <\/p>\n

        We get,<\/span><\/p>\n

        R1.<\/sub>Rx<\/sub> \u2013 j.(R1<\/sub>\/ w.Cx<\/sub>) = R2<\/sub>.R3<\/sub> \u2013 j.( R2<\/sub>\/ w.C3<\/sub>) —- (10)<\/span><\/p>\n

         <\/p>\n

        On equating the real parts, we get<\/span><\/p>\n

        R1<\/sub>. Rx<\/sub> = R2<\/sub>.R3<\/sub> ——– (11)<\/span><\/p>\n

        Rx<\/sub> = (R2<\/sub>.R3<\/sub>)\/ R1<\/sub> ——-(12)<\/span><\/p>\n

         <\/p>\n

        On equating the imaginary parts<\/span><\/p>\n

        R1<\/sub>\/(w.Cx<\/sub>) = R2<\/sub>\/(w.C3<\/sub>) —— (13)<\/span><\/p>\n

         <\/p>\n

        Cx<\/sub> =(C3<\/sub>.R1<\/sub>)\/R1<\/sub> —— (14)<\/span><\/p>\n<\/div>\n

        \n

         <\/p>\n

        Therefore from equations 12 & 14 one can determine the value of unknown capacitor and its leakage resistance. Experimentally true balance can be obtained by varying R1 and R3 simultaneously.<\/p>\n

         <\/p>\n

        Another type of AC bridge is<\/p>\n

         <\/p>\n

        Wein Bridge<\/strong><\/p>\n

         <\/p>\n

        A variant of Capacitance Bridge is <\/span>Wein Bridge,<\/em> which has 4 resistors and two capacitors. It is important to note this bridge does not require equal values of R & C. In one arm we have RC combination in series and in the adjacent arm its\u2019 in a parallel combination. This bridge is designed to measure frequency and is used for measuring unknown capacitor with great accuracy. The arm in which capacitor is in parallel to variable resistor R3, admittance value is used rather than impedance.<\/span><\/p>\n<\/div>\n

        \n

        \"\"<\/p>\n

         <\/p>\n

        Figure 2. <\/strong>Circuit Diagram of Wein Bridge. It has two variable resistors R1 <\/sub>and R3<\/sub> and two fixed resistor R2<\/sub> & R4<\/sub>. Capacitor C3<\/sub> is parallel to R3<\/sub> and Capacitor C1<\/sub> is in series with R1<\/sub>.<\/p>\n

         <\/p>\n

         <\/p>\n

        Admittance for the arm is written as \u2013<\/p>\n

         <\/p>\n

        Y3<\/sub> = 1\/R3<\/sub> + j.w.C3<\/sub> ———- (15)<\/span><\/p>\n

         <\/p>\n

        In the balance equation Z3 is replaced by 1\/Y3<\/sub><\/p>\n

        Therefore balance equation can be written as \u2013<\/p>\n

         <\/p>\n

        Z1<\/sub>. Z4<\/sub> = Z2<\/sub>\/Y3<\/sub>, i.e. Z2<\/sub> = Z1<\/sub>. Z4<\/sub>.Y3<\/sub><\/p>\n

         <\/p>\n

        On substituting and rearranging the terms we get \u2013<\/p>\n

         <\/p>\n

        \"\"\u00a0 \u00a0By equating real and imaginary terms we get \u2013<\/p>\n<\/div>\n

        \"\"<\/p>\n

        \n

         <\/p>\n

        The bridge can be used for measuring frequency within the audio range. Here R1 & R3 are kept at identical values and capacitors are normally of fixed values.<\/p>\n

         <\/p>\n

        There are two conditions under which bridge is balanced, i.e. equation 18 determines the required resistance ratio R1\/R4 and equation 20 is used to determine frequency of the applied voltage. This means if we balance the resistance ratio in equation 18 and simultaneously excite the bridge at a frequency given in equation 20, the bridge will get balanced.<\/p>\n

         <\/p>\n

        For a Wein bridge, circuits components are chosen such that R1<\/sub> = R3<\/sub> =R and C1<\/sub> = C2<\/sub>= C. For equation 18, it reduces ratio R1<\/sub>\/R2<\/sub> =2 and frequency equation 20 to f= 1\/2 RC<\/em>. The bridge can measure frequencies within the audio range. The frequencies with the audio range are divided into 20-200, 200-2000, 2000-20kHz ranges. Here, resistances are modulated to change the frequency range and further fine control within the range\u00a0is obtained by adjusting capacitors C1<\/sub> &C2<\/sub>. If one desires to measure capacitances, in that <\/span>case frequency of operation of the AC Source should be known.<\/span><\/p>\n

         <\/p>\n

        The bridge can also be used as Harmonic distortion analyzer or as a Notch Filter. The bridge is used as <\/span>frequency determining element in audio and radio frequency oscillators. With Wein Bridge, <\/span>accuracy of 0.5%-1% can be readily obtained but since the bridge is frequency sensitive, it is difficult to obtained balance unless the applied voltage waveform is purely sinusoidal.<\/span><\/p>\n

         <\/p>\n

        Now we will study about<\/span>..<\/p>\n

         <\/p>\n

        Inductance Comparison Bridge<\/strong><\/p>\n

         <\/p>\n

        Inductance Comparison Bridge is similar to Capacitance Comparison Bridge, <\/span>only difference being the replacement of capacitors with inductors. This bridge is used for measuring unknown inductance Lx<\/sub> and its internal resistance Rx<\/sub>. It has two pure resistances R1<\/sub> & R2<\/sub>, a variable resistor R3<\/sub> with inductor L3<\/sub> and an unknown inductor Lx<\/sub> having an internal resistance Rx.<\/span><\/p>\n

         <\/p>\n

        As discussed for capacitance, the impedance for an inductor can be written as –<\/span><\/p>\n

         <\/p>\n

        Z = R + j(w.L) \uf057 ——— (21)<\/span><\/p>\n<\/div>\n

        \n

        \"\"<\/p>\n

         <\/p>\n

        Figure 3<\/strong>. Circuit diagram for Inductance Comparison Bridge On substituting equation 21 into the balanced impedance equation 5 we get –<\/p>\n

         <\/p>\n

        R1<\/sub>.Rx<\/sub> + j .w.R1<\/sub>.Lx = R2<\/sub>.R3<\/sub> – j .w.R2<\/sub>.L3<\/sub> —- (22)<\/p>\n

         <\/p>\n

        On equating the real parts we get \u2013<\/p>\n

         <\/p>\n

        Rx<\/sub> = (R2<\/sub>.R3<\/sub>)\/R1<\/sub>\u00a0 ——– (23)<\/p>\n

         <\/p>\n

        On equating the imaginary parts we get \u2013<\/p>\n

         <\/p>\n

        Lx<\/sub> = (R2<\/sub>. L3<\/sub>)\/R1<\/sub> ——— (24)<\/span><\/p>\n<\/div>\n

        \n

         <\/p>\n

        To the balance the bridge, inductive balance control is achieved by R2<\/sub> and resistance balance control is achieved by R3<\/sub>. By alternatingly varying the L3<\/sub> or R3<\/sub> the balance for the inductance comparison bridge is obtained<\/p>\n

         <\/p>\n

        Resonance Bridge<\/strong><\/p>\n

        \"\"<\/p>\n

         <\/p>\n

        Figure. 4. <\/strong>\u2013 Circuit diagram for Resonance Bridge<\/p>\n

         <\/p>\n

        A resonance bridge is a third category of bridge that contains a resistor (Rx<\/sub>), capacitor (Cx<\/sub>) and an inductor (Lx<\/sub>) in series in one of its arms. Other three arms consist of resistor only. On substituting values to bridge balance equation we get \u2013<\/p>\n

         <\/p>\n

        R1<\/sub>. (Rx<\/sub> +j.w.Lx \u2013 j\/(jCx)) = R2.R3 —- (30)<\/p>\n

         <\/p>\n

        On equating real terms we get \u2013<\/p>\n

         <\/p>\n

        Rx = (R2.R3)\/R1 ——–(31)<\/span><\/p>\n

         <\/p>\n

        On equating imaginary terms we get \u2013<\/span><\/p>\n

         <\/p>\n

        j.w.Lx \u2013 j\/(w.Cx) = 0<\/span><\/p>\n

         <\/p>\n

        w2<\/sup>= 1\/(Lx.Cx) ———- (32)<\/span><\/p>\n<\/div>\n

        Resonant frequency of this series resonance circuit can be calculated with the following equation \u2013<\/span><\/p>\n

         <\/p>\n

        \n

        \"\"<\/p>\n

        For measuring unknown inductor, a standard capacitor is varied until balance is obtained then \u2013<\/p>\n

         <\/p>\n

        Lx = 1\/(w2<\/sup>. Cx) ———– (34)<\/span><\/p>\n

         <\/p>\n

        For measuring unknown capacitor, a standard inductance is varied until balance is obtained then \u2013<\/p>\n

         <\/p>\n

        Cx = 1\/(w2<\/sup>. Lx) ————– (35)<\/span><\/p>\n

         <\/p>\n

        It is important to note that operating frequency of the generator should be known in order to find out an unknown quantity.<\/p>\n

         <\/p>\n

        Digital Readout Bridge<\/strong><\/p>\n

         <\/p>\n

        \"\"<\/p>\n

         <\/p>\n

        Figure 5. <\/strong>Block diagram of Wheatstone Bridge with Digital Readout<\/p>\n

         <\/p>\n

        With advent of digital circuitry there is tremendous effect on electronic testing instruments. Use of digital circuits has helped in developing Digital Readout Bridge.\u00a0Bridge\u2019s configuration i.e. actual measuring circuitry hasn\u2019t <\/span>change much and this system has also removed operator error while observing the reading. The diagram shown in figure 5 is of a Wheatstone bridge with a digital readout circuit. From the diagram one can observe that a logic circuit provides a signal to R3, it senses the null and provides a representing value for Rx.<\/span><\/p>\n

         <\/p>\n

        There are different\u2026.<\/span><\/p>\n

         <\/p>\n

        Types of Detectors, <\/strong>– based on their application and frequency range is given below\u2026<\/span><\/p>\n

          \n
        1. At low frequency, <\/span>best detector is vibrational galvanometer.<\/span><\/li>\n
        2. For laboratory work and frequencies upto 100 Hz, moving coil type is the most preferred <\/span>due its high sensitivity.<\/span><\/li>\n
        3. For frequencies between 300 Hz- 1 kHz, and for high voltages, moving magnet type vibrational galvanometer with remote controlled tuning are preferred.<\/span><\/li>\n
        4. For audio frequencies greater than 800 Hz, headphones are best detector. It is important to note that vibrational galvanometers and headphones do not have phase sensitivity. That means they cannot indicate whether resistance or reactance adjustment is required.<\/span><\/li>\n
        5. At low frequencies and for high sensitivity, ac galvanometer and separately excited dynamometer having phase sensitivity are best suited.<\/span><\/li>\n
        6. For routine measurement of bridges, pointer instruments are used. It is more advantageous if such instruments are made phase selective. Predominantly Pointer instruments are moving coil milliammeters and are operated via some arrangement of copper oxide rectifiers. And have a working range of (40 Hz-1 kHz)<\/li>\n
        7. Modern bridges are regularly fitted with an amplifier<\/li>\n
        8. A heterodyne or beat-tone detector are used for high audio or radio frequencies, or frequencies above 3 kHz<\/li>\n
        9. For almost all bridges, impedance should be selected that best suits the bridge. An Interbridge transformer can help in obtaining higher sensitivity. When using a headphone as a detector, one must take precaution to eliminate any capacitance effects between the observer and the headphones.<\/span><\/li>\n
        10. The range of moving magnet vibration galvanometer is up to 1500 Hz.<\/li>\n
        11. As an ac detector, an electrodynamometer can also be used.<\/li>\n
        12. Small capacitances have very large impedance, especially in an ac circuit at low frequency and when measured in a bridge they tend to form a high impedance branch. Hence, electrometer is used as a detector to increase sensitivity.<\/li>\n<\/ol>\n<\/div>\n

          \u00a0 \u00a0 Summary<\/strong><\/p>\n

          In this module we studied about AC bridge circuits.<\/p>\n

            \n
          1. First we looked into classification of AC bridges in the introduction.<\/li>\n
          2. Under AC Bridges we studied about capacitance comparison bridge and its variant Wein Bridge<\/li>\n
          3. And then we studied about Inductance Comparison Bridge and Resonance Bridge Circuit<\/li>\n<\/ol>\n\n\n\n
            you can view video on Bridges Controlled Circuits – II<\/strong><\/td>\n\"\"<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

            \u00a0 \u00a0\u00a0References :-<\/strong><\/p>\n

              \n
            1. Electrical and Electronic Measurements and Instrumentation, Sawhney A. K.<\/em>, Dhanpat Rai & Sons, Reprint 1985<\/li>\n
            2. Measurements and Instrumentation, Bakshi U.A., Bakshi A.V.,<\/em> Technical Publications, 2009<\/li>\n
            3. Principles of instrumental analysis, Skoog, Douglas A., F. James Holler, and<\/em> Stanley R. Crouc,. <\/em>Cengage learning, Edition 2017<\/li>\n
            4. Instrumentation, measurement and analysis. Nakra, B.C. and Chaudhry, K.K.,<\/em> Tata McGraw-Hill Education, 2003.<\/li>\n
            5. Measurement and instrumentation: theory and application, Morris, A. S., &<\/em> Langari, R<\/em>. , Academic Press, 2012.<\/li>\n<\/ol>\n","protected":false},"author":3,"menu_order":2,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-vinay-gupta"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-37","chapter","type-chapter","status-publish","hentry","contributor-prof-vinay-gupta"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/37","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":7,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/37\/revisions"}],"predecessor-version":[{"id":501,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/37\/revisions\/501"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/37\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/media?parent=37"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapter-type?post=37"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/contributor?post=37"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/license?post=37"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}