A **bridge circuit** is a topology of electrical circuitry in which two circuit branches (usually in parallel with each other) are "bridged" by a third branch connected between the first two branches at some intermediate point along them. The bridge was originally developed for laboratory measurement purposes and one of the intermediate bridging points is often adjustable when so used. Bridge circuits now find many applications, both linear and non-linear, including in instrumentation, filtering and power conversion.^{ [1] }^{ [2] }

The best-known bridge circuit, the Wheatstone bridge, was invented by Samuel Hunter Christie and popularized by Charles Wheatstone, and is used for measuring resistance. It is constructed from four resistors, two of known values R_{1} and R_{3} (see diagram), one whose resistance is to be determined R_{x}, and one which is variable and calibrated R_{2}. Two opposite vertices are connected to a source of electric current, such as a battery, and a galvanometer is connected across the other two vertices. The variable resistor is adjusted until the galvanometer reads zero. It is then known that the ratio between the variable resistor and its neighbour R1 is equal to the ratio between the unknown resistor and its neighbour R3, which enables the value of the unknown resistor to be calculated.

The Wheatstone bridge has also been generalised to measure impedance in AC circuits, and to measure resistance, inductance, capacitance, and dissipation factor separately. Variants are known as the Wien bridge, Maxwell bridge, and Heaviside bridge (used to measure the effect of mutual inductance). ^{ [3] } All are based on the same principle, which is to compare the output of two potential dividers sharing a common source.

In power supply design, a bridge circuit or bridge rectifier is an arrangement of diodes or similar devices used to rectify an electric current, i.e. to convert it from an unknown or alternating polarity to a direct current of known polarity.

In some motor controllers, an H-bridge is used to control the direction the motor turns.

From the figure to the right, the bridge current is represented as **I _{5}**

Per Thévenin's theorem, finding the **Thevenin** equivalent circuit which is connected to the bridge load **R _{5}** and using the arbitrary current flow

Thevenin Source (**V _{th}**) is given by the formula:

and the Thevenin resistance (**R _{th}**):

Therefore the current flow (**I _{5}**) through the bridge is given by Ohm's law:

and the voltage (**V _{5}**) across the load (

- Phantom circuit - a use of balanced bridge circuits in telephony
- Lattice filter - an application of bridge topology to all-pass filters

An **ammeter** is an instrument used to measure the current in a circuit. Electric currents are measured in amperes (A), hence the name. For direct measurement, the ammeter is connected in series with the circuit in which the current is to be measured. An ammeter usually has low resistance so that it does not cause a significant voltage drop in the circuit being measured.

A **Wheatstone bridge** is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. The primary benefit of the circuit is its ability to provide extremely accurate measurements. Its operation is similar to the original potentiometer.

In electrical engineering, the **power factor** of an AC power system is defined as the ratio of the *real power* absorbed by the load to the *apparent power* flowing in the circuit. Real power is the average of the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of RMS current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power, so more current flows in the circuit than would be required to transfer real power alone. A power factor magnitude of less than one indicates the voltage and current are not in phase, reducing the average product of the two. A negative power factor occurs when the device generates real power, which then flows back towards the source.

A **rectifier** is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction. The reverse operation is performed by an inverter.

A **potentiometer** is a three-terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider. If only two terminals are used, one end and the wiper, it acts as a **variable resistor** or **rheostat**.

In direct-current circuit theory, **Norton's theorem**, also called the **Mayer–Norton theorem**, is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the network, it can be replaced by a current source and a single resistor in parallel.

As originally stated in terms of direct-current resistive circuits only, **Thévenin's theorem** states that *"Any linear electrical network containing only voltage sources, current sources and resistances can be replaced at terminals A–B by an equivalent combination of a voltage source V _{th} in a series connection with a resistance R_{th}."*

Two-terminal components and electrical networks can be connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology. Whether a two-terminal "object" is an electrical component or an electrical network is a matter of perspective. This article will use "component" to refer to a two-terminal "object" that participate in the series/parallel networks.

In electronics, a **voltage divider ** is a passive linear circuit that produces an output voltage (*V*_{out}) that is a fraction of its input voltage (*V*_{in}). **Voltage division** is the result of distributing the input voltage among the components of the divider. A simple example of a voltage divider is two resistors connected in series, with the input voltage applied across the resistor pair and the output voltage emerging from the connection between them.

A **gyrator** is a passive, linear, lossless, two-port electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the resistor, capacitor, inductor and ideal transformer. Unlike the four conventional elements, the gyrator is non-reciprocal. Gyrators permit network realizations of two-(or-more)-port devices which cannot be realized with just the conventional four elements. In particular, gyrators make possible network realizations of isolators and circulators. Gyrators do not however change the range of one-port devices that can be realized. Although the gyrator was conceived as a fifth linear element, its adoption makes both the ideal transformer and either the capacitor or inductor redundant. Thus the number of necessary linear elements is in fact reduced to three. Circuits that function as gyrators can be built with transistors and op-amps using feedback.

A network, in the context of electrical engineering and electronics, is a collection of interconnected components. **Network analysis** is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values. However, for the most part, the techniques assume linear components. Except where stated, the methods described in this article are applicable only to *linear* network analysis.

A **two-port network** is an electrical network (circuit) or device with two *pairs* of terminals to connect to external circuits. Two terminals constitute a port if the currents applied to them satisfy the essential requirement known as the port condition: the electric current entering one terminal must equal the current emerging from the other terminal on the same port. The ports constitute interfaces where the network connects to other networks, the points where signals are applied or outputs are taken. In a two-port network, often port 1 is considered the input port and port 2 is considered the output port.

A **Wien bridge oscillator** is a type of electronic oscillator that generates sine waves. It can generate a large range of frequencies. The oscillator is based on a bridge circuit originally developed by Max Wien in 1891 for the measurement of impedances. The bridge comprises four resistors and two capacitors. The oscillator can also be viewed as a positive gain amplifier combined with a bandpass filter that provides positive feedback. Automatic gain control, intentional non-linearity and incidental non-linearity limit the output amplitude in various implementations of the oscillator.

The **negative impedance converter** (**NIC**) is an active circuit which injects energy into circuits in contrast to an ordinary load that consumes energy from them. This is achieved by adding or subtracting excessive varying voltage in series to the voltage drop across an equivalent positive impedance. This reverses the voltage polarity or the current direction of the port and introduces a phase shift of 180° (inversion) between the voltage and the current for any signal generator. The two versions obtained are accordingly a *negative impedance converter with voltage inversion* (VNIC) and a *negative impedance converter with current inversion* (INIC). The basic circuit of an INIC and its analysis is shown below.

**Ripple** in electronics is the residual periodic variation of the DC voltage within a power supply which has been derived from an alternating current (AC) source. This ripple is due to incomplete suppression of the alternating waveform after rectification. Ripple voltage originates as the output of a rectifier or from generation and commutation of DC power.

A **Maxwell bridge** is a modification to a Wheatstone bridge used to measure an unknown inductance in terms of calibrated resistance and inductance or resistance and capacitance. When the calibrated components are a parallel resistor and capacitor, the bridge is known as a **Maxwell-Wien** bridge. It is named for James C. Maxwell, who first described it in 1873.

**Zobel networks** are a type of filter section based on the image-impedance design principle. They are named after Otto Zobel of Bell Labs, who published a much-referenced paper on image filters in 1923. The distinguishing feature of Zobel networks is that the input impedance is fixed in the design independently of the transfer function. This characteristic is achieved at the expense of a much higher component count compared to other types of filter sections. The impedance would normally be specified to be constant and purely resistive. For this reason, Zobel networks are also known as constant resistance networks. However, any impedance achievable with discrete components is possible.

A **Kelvin bridge**, also called a **Kelvin double bridge** and in some countries a **Thomson bridge**, is a measuring instrument used to measure unknown electrical resistors below 1 ohm. It is specifically designed to measure resistors that are constructed as four terminal resistors.

A **potentiometer** is an instrument for measuring voltage or 'potential difference' by comparison of an unknown voltage with a known reference voltage. If a sensitive indicating instrument is used, very little current is drawn from the source of the unknown voltage. Since the reference voltage can be produced from an accurately calibrated voltage divider, a potentiometer can provide high precision in measurement. The method was described by Johann Christian Poggendorff around 1841 and became a standard laboratory measuring technique.

The **transformer ratio arm bridge** or **TRA bridge** is a type of bridge circuit used for measuring electronic components, using a.c. It can be designed to work in terms of either impedance or admittance. It can be used on resistors, capacitors and inductors, measuring minor as well as major terms, e.g. series resistance in capacitors. It is probably the most accurate type of bridge available, being capable of the precision needed, for example, when checking secondary component standards against national standards.

- ↑ Bureau of Naval Personnel,
*Basic Electricity*, p.114, Courier Dover Publications, 1970 ISBN 0-486-20973-3. - ↑ Clarence W. De Silva,
*Vibration monitoring, testing, and instrumentation*, pp.2.43-2.49, CRC Press, 2007 ISBN 1-4200-5319-1 - ↑ All about circuits: AC bridge circuits

- Jim Williams, "Bridge circuits: Marrying gain and balance", Linear Technology Application Note 43, June 1990.
- Bridge circuits - Chapter 8 from an online book.

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