### AC Bridges: Contents

**Recall AC Bridges and types of AC Bridges used for the Measurement of Parameters** 1

**Recall the types of Detectors used in AC Bridges** 2

**Derive the general equation for Bridge Balance** 3

**Recall the Dissipation Factor in Capacitance** 6

**Recall the Applications of Wein’s Bridge** 9

**Recall the Limitations of Wien’s Bridge** 10

**Recall AC Bridges and types of AC Bridges used for the Measurement of Parameters**

AC bridges are electrical circuits used to measure the values of various parameters, such as resistance, inductance, capacitance, and impedance, with high accuracy. These bridges operate based on the principle of comparing the unknown component with a known component in a balanced condition.

There are several types of AC bridges used for the measurement of parameters. The common types include:

- Wheatstone Bridge: The Wheatstone bridge is the most basic and widely used AC bridge. It is primarily used to measure resistance accurately by comparing the unknown resistance with known resistors. The bridge is balanced when the ratio of the resistances on one side is equal to the ratio on the other side.
- Maxwell Bridge: The Maxwell bridge is used to measure the value of an unknown inductance. It compares the unknown inductance with a known inductance and uses a variable capacitor to balance the bridge. The bridge is balanced when the ratios of the inductances and resistances are equal.
- Schering Bridge: The Schering bridge is specifically designed to measure the capacitance of unknown capacitors. It compares the unknown capacitor with a known capacitor and balances the bridge using a variable resistor. The bridge is balanced when the ratios of the capacitances and resistances are equal.
- Anderson Bridge: The Anderson bridge is used for measuring the impedance of an unknown component, which can be a combination of resistance, inductance, and capacitance. It provides a balanced condition by adjusting the frequency and the ratio of the resistances and reactances.
- Hay Bridge: The Hay bridge is primarily used to measure the impedance of unknown inductors, including their resistance and inductance components. It uses a combination of resistors, capacitors, and inductors in the bridge circuit to achieve balance.

These AC bridges provide accurate measurements by achieving a balanced condition where the bridge output becomes zero or minimum. The measurement can then be calculated based on the known and unknown components involved in the balanced condition of the bridge.

**Recall the types of Detectors used in AC Bridges**

In AC bridges, various types of detectors are used to measure the null or balance condition of the bridge circuit. The detectors are responsible for indicating when the bridge is balanced, which helps in accurately measuring the unknown component or parameter.

The common types of detectors used in AC bridges include:

- Galvanometer: A galvanometer is a sensitive current measuring device that detects the flow of current in the bridge circuit. It can be used as a null detector in AC bridges by indicating zero current when the bridge is balanced.
- Electronic Detectors: Electronic detectors such as operational amplifiers (op-amps) or specialized electronic circuits are often used in modern AC bridges. These detectors can amplify the small voltage or current signals generated by the bridge and provide an output indication when the bridge is balanced.
- Vacuum Tube Detectors: In some older AC bridges, vacuum tube-based detectors such as diode detectors or vacuum tube voltmeters (VTVMs) are employed. These detectors utilize the non-linear characteristics of vacuum tubes to convert the AC signal into a DC voltage or to provide an indication of balance in the bridge.
- Digital Detectors: With the advancement of technology, digital detectors have also been used in AC bridges. These detectors typically involve analog-to-digital converters (ADCs) or digital signal processing (DSP) techniques to measure and analyze the signals from the bridge circuit.

The choice of detector depends on the specific requirements of the AC bridge circuit, the desired sensitivity, accuracy, and the availability of suitable detection methods.

**Derive the general equation for Bridge Balance**

The general equation for bridge balance in an AC bridge is given by:

Z1/Z2 = Z3/Z4

Where Z1, Z2, Z3, and Z4 are the impedances of the four arms of the bridge.

At balance, the bridge current I is zero, and the voltage across the galvanometer Vg is also zero. Therefore, the voltage drop across arm 1 (V1) and arm 3 (V3) are equal, and the voltage drop across arm 2 (V2) and arm 4 (V4) are also equal. This can be expressed mathematically as:

V1 = V3, and V2 = V4

Using Ohm’s law, the voltage drop across each arm of the bridge can be expressed in terms of the impedances and the current as follows:

V1 = I Z1, V2 = I Z2, V3 = I Z3, and V4 = I Z4

Substituting these equations into the equation for balance, we get: (I Z1)/(I Z2) = (I Z3)/(I Z4)

Simplifying and cancelling out the current I, we get: Z1/Z2 = Z3/Z4

This is the general equation for bridge balance in an AC bridge. When the impedances of the four arms of the bridge satisfy this equation, the bridge is balanced and the unknown parameter can be accurately measured.

**Describe the following Bridges for the measurement of Inductances: Maxwell’s Bridge and Hay’s Bridge**

- Maxwell’s Bridge:

Maxwell’s bridge is an AC bridge circuit used to measure the value of an unknown inductance. It is particularly useful for measuring inductances with high Q factors. The bridge consists of four arms: two known resistors (R1 and R2), a variable capacitor (C), and the unknown inductance (Lx). The bridge is balanced when the ratio of the resistances (R1/R2) is equal to the ratio of the reactances (ωLx/1/ωC), where ω is the angular frequency of the AC source. At balance, the bridge can be represented by the equation:

R1/R2 = ωLx/1/ωC

By measuring the values of R1, R2, and C and adjusting the variable capacitor until the bridge is balanced, the unknown inductance Lx can be determined.

- Hay’s Bridge:

Hay’s bridge is another AC bridge circuit used for measuring inductances. It is commonly employed for measuring inductances with lower Q factors. The bridge consists of four arms: a known resistance (R1), a known inductance (L1), an unknown inductance (Lx), and a variable resistor (R2). The bridge is balanced when the product of the resistances (R1R2) is equal to the product of the inductances (L1Lx), and the variable resistor is adjusted accordingly. The balance equation of Hay’s bridge can be expressed as:

R1R2 = L1Lx

By measuring the values of R1, R2, and L1 and adjusting the variable resistor until the bridge is balanced, the unknown inductance Lx can be determined.

Both Maxwell’s bridge and Hay’s bridge provide a means to accurately measure unknown inductances by achieving a balanced condition in the bridge circuit. The balance condition is achieved by adjusting the variable component (capacitor in Maxwell’s bridge and resistor in Hay’s bridge) until the bridge output becomes zero or minimum, allowing for precise measurement of the unknown inductance.

**Describe the following Bridges for the measurement of Inductances: Anderson’s Bridge and Owen’s Bridge**

- Anderson’s Bridge:

Anderson’s bridge is an AC bridge circuit used for the measurement of inductances. It is specifically designed for the measurement of low-Q inductors. The bridge consists of four arms: a known resistance (R1), a variable resistance (R2), an unknown inductance (Lx), and a known capacitor (C). The bridge is balanced when the ratio of the resistances (R1/R2) is equal to the ratio of the reactances (ωLx/1/ωC), where ω is the angular frequency of the AC source. At balance, the bridge can be represented by the equation:

R1/R2 = ωLx/1/ωC

By measuring the values of R1, R2, C, and adjusting the variable resistor until the bridge is balanced, the unknown inductance Lx can be determined.

- Owen’s Bridge:

Owen’s bridge is an AC bridge circuit used for the measurement of inductances. It is particularly suitable for the measurement of high-Q inductors. The bridge consists of four arms: a known resistance (R1), a variable resistance (R2), an unknown inductance (Lx), and a known capacitor (C). The bridge is balanced when the ratio of the resistances (R1/R2) is equal to the ratio of the reactances (ωLx/1/ωC), where ω is the angular frequency of the AC source. At balance, the bridge can be represented by the equation:

R1/R2 = ωLx/1/ωC

Similar to Anderson’s bridge, by measuring the values of R1, R2, C, and adjusting the variable resistor until the bridge is balanced, the unknown inductance Lx can be determined.

Both Anderson’s bridge and Owen’s bridge are AC bridge circuits used for the measurement of inductances. They operate based on the principle of balancing the bridge circuit by adjusting the variable resistance until the bridge is balanced. By achieving balance, the unknown inductance can be accurately determined using the known components of the bridge circuit.

**Recall the Dissipation Factor in Capacitance**

The dissipation factor, also known as the loss angle tangent or tan delta, is a measure of the energy lost in a capacitor due to internal factors such as resistance, dielectric losses, and leakage currents. It is defined as the ratio of the capacitive reactance (Xc) to the equivalent series resistance (ESR) of the capacitor:

Dissipation Factor = tan(delta) = ESR / Xc

where Xc = 1 / (2 * pi * f * C) is the capacitive reactance, f is the frequency of the applied voltage, and C is the capacitance of the capacitor.

The dissipation factor is a dimensionless quantity that is typically expressed as a percentage or in terms of its tangent. It is often used as a measure of the quality of a capacitor, with lower values indicating a capacitor that is more efficient and has lower losses.

The dissipation factor is commonly measured using a device called a bridge or metre that applies an AC voltage to the capacitor and measures the phase difference between the applied voltage and the resulting current. The phase difference is related to the dissipation factor through the tangent function, allowing the dissipation factor to be calculated from the measured values.

**Describe De-Sauty Bridge**

The De-Sauty bridge is an AC bridge circuit used for the measurement of capacitance. It was developed by Marcel De-Sauty and is based on the principle of balancing the bridge circuit to determine the unknown capacitance.

The De-Sauty bridge consists of four arms: a variable resistance (R1), a known resistance (R2), an unknown capacitance (Cx), and a known inductance (L). The bridge is balanced when the ratio of the resistances (R1/R2) is equal to the ratio of the reactances (1/ωCx) and (ωL), where ω is the angular frequency of the AC source. At balance, the bridge can be represented by the equation:

R1/R2 = 1/ωCx / ωL

By measuring the values of R1, R2, L, and adjusting the variable resistor until the bridge is balanced, the unknown capacitance Cx can be determined.

The De-Sauty bridge is known for its accuracy in measuring capacitance values and is commonly used in laboratories and research settings. It is particularly suitable for measuring small capacitance values and can provide precise results when the bridge is properly balanced.

**Describe Schering Bridge**

The Schering bridge is an AC bridge used for measuring the capacitance and dielectric loss of a capacitor. It consists of four arms, two of which contain known resistances, one arm contains the unknown capacitance, and the fourth arm contains a series combination of a variable resistor and a known capacitor.

To measure the capacitance, the variable resistor is adjusted until the bridge is balanced, which is indicated by zero current flowing through the detector. At balance, the ratio of the two known resistances is equal to the ratio of the unknown capacitance to the known capacitor and the capacitance value can be calculated. To measure the dielectric loss, the bridge is balanced at a specific frequency and the value of the variable resistor is noted. The dielectric loss can be calculated using the formula:

tan δ = R / (2πfC)

where tan δ is the dielectric loss, R is the resistance in the variable arm, f is the frequency, and C is the capacitance of the unknown capacitor.

**Describe Wein’s Bridge**

Wein’s bridge is an AC bridge used for measuring the frequency of an unknown AC signal. It is based on the principle of resonance and consists of four arms, two of which contain known resistors, one arm contains an unknown capacitor, and the fourth arm contains a series combination of a variable resistor and a known resistor.

At the resonant frequency, the bridge is balanced, and the ratio of the two known resistors is equal to the ratio of the unknown capacitor to the variable resistor. The resonant frequency can be calculated using the formula:

f = 1 / (2πRC)

where f is the resonant frequency, R is the resistance in the variable arm, and C is the capacitance of the unknown capacitor.

**Recall the Applications of Wein’s Bridge**

Wein’s bridge is a type of AC bridge circuit that is commonly used in electronic applications to measure the impedance of a circuit or component at a specific frequency. The circuit is named after its inventor, Max Wien.

Some of the common applications of Wein’s bridge are:

- Measurement of Capacitance: Wien’s bridge can be used to measure the capacitance of an unknown capacitor by comparing it with a known capacitor. By adjusting the frequency of the AC source, the bridge can be balanced and the value of the unknown capacitor can be calculated.
- Measurement of Inductance: Wein’s bridge can also be used to measure the inductance of an unknown inductor by comparing it with a known inductor. Again, by adjusting the frequency of the AC source, the bridge can be balanced and the value of the unknown inductor can be calculated.
- Audio Frequency Oscillator: Wein’s bridge can be used as an audio frequency oscillator by using a feedback loop to provide a sustained oscillation at a specific frequency. This oscillator is commonly used in audio applications, such as generating tones or test signals.
- Active Filters: Wein’s bridge can be used in the design of active filters, which are circuits that filter out unwanted frequencies from a signal. By using the bridge to measure the impedance of a circuit at a specific frequency, the filter can be designed to provide the desired frequency response.

Overall, Wein’s bridge is a versatile circuit that is widely used in electronic applications to measure and analyse circuits and components at a specific frequency.

**Recall the Limitations of Wien’s Bridge**

Wein’s bridge is a useful circuit for measuring the impedance of a circuit or component at a specific frequency. However, it has some limitations that should be considered when using it in practical applications. Some of the limitations of Wein’s bridge are:

- Limited Frequency Range: Wein’s bridge is designed to work at a specific frequency, and its accuracy is limited to that frequency. If the frequency of the AC source is changed, the balance of the bridge will be disturbed, and the accuracy of the measurements will be affected.
- Sensitivity to Temperature: The accuracy of Wein’s bridge is sensitive to changes in temperature. The resistance and reactance of the components in the bridge can vary with temperature, which can affect the balance of the bridge and the accuracy of the measurements.
- Limited Accuracy: The accuracy of Wein’s bridge is limited by the accuracy of the components used in the circuit. The tolerances of the resistors and capacitors used in the bridge can affect the balance of the circuit and the accuracy of the measurements.
- Limited Applicability: Wein’s bridge is primarily designed for measuring the impedance of passive components such as capacitors and inductors. It may not be suitable for measuring the impedance of active components or circuits, such as amplifiers or filters.