The tension divider is a simple electronic assembly which makes it possible to divide a tension of entry. A circuit made up of two resistances in series is for example an elementary assembly which can carry out this operation. It is usually used to create a reference voltage standard or attenuator of low frequency signal.

Principle of the tension divider

Tension divider noncharged

Tension divider noncharged

The tensions of the divider are connected to the mass and two resistances R_{1} and R_{2} are connected in series. A tension U is applied in entry to these two resistances and the output voltage is measured at the boundaries of R_{2}.

By using the Law of Ohm with the tensions U and U_{2}, it is possible to deduce the relation between the output voltage U_{2} and the tension from entry U

- U = I * (R
_{1}+ R_{2}) - U
_{2}= I * R_{2} - I = U * (1 ⁄ R
_{1}+ R_{2}) - U
_{2}= U * (R_{2}⁄ R_{1}+ R_{2})

Principle of the tension divider charged

Pont tension divider with a load

Pont tension divider with a load

The assembly is similar to the precedent but with at exit a load RL. This one is in parallel with R_{2} resistance. The equivalent resistance seen by U_{2} is thus expressed by:

R_{eq} = (R_{2} * R_{L}) ⁄ (R_{2} + R_{L})

The equation of the tension divider can then be written:

U_{2} = U * (R_{eq} ⁄ R_{1} + R_{eq}) = U * (R_{2} * R_{L} ⁄ R_{1} * R_{2} + R_{1} * R_{L} + R_{2} * R_{L})

It should be noted that if R_{2} is negligible in front of load R_{L} then Req R_{2} and the divider behaves roughly like an assembly without load.

A divider of current is a simple electronic assembly making it possible to obtain a current proportional to another current. The circuit consists of parallel branches and is studied thanks to the laws of Kirchhoff and in particular with the law of the nodes.

General information

The formula of the divider of current makes it possible to calculate the intensity of the current in a resistance when this one belonged to a whole of resistances in parallel and when one knows the total current which feeds this unit.

Example of dividing bridge of current.

Here a simple node and on its line the formula corresponding to this node : I_{1} = I * R_{2} ⁄ R_{1} + R_{2}

Many electronic applications require a continuous supply voltage. To convert an alternating voltage into continuous tension, one uses a bridge of diodes, called bridge of Graetz.

The bridge of Graetz is made of 4 diodes. There are two entries where the alternating voltage (secondary of a transformer or sector) and the exits must arrive "+" and" - "where leaves the tension continues. In fact, this tension is not continuous, but it is of constant sign. With the oscilloscope, one sees the function "value absolute of a sine". A condenser of filtering is often added between "+" and it" - "bridge to smooth the tension.

Principle of operation

Two cases are to be considered according to the sign of the alternating voltage of entry.

If the tension of entry is positive, D1 and D4 are busy. D2 and D3 are blocked. The current crosses from top to bottom the resistance (which represents the load), of "+" towards" - ".

If the tension of entry is negative, D2 and D3 are busy. D1 and D4 are blocked. The current crosses in the same way from top to bottom the resistance (which represents the load), of "+" towards" - ".

The direction of the current in resistance is thus constant, it is the role of the bridge of Graetz.

Advantages of the bridge:

Setting with profit of two alternations of the tension, contrary with a simple diode

Maximum opposite tension Vmax (and not 2.Vmax like a simple diode)

Disadvantages of the bridge:

Fall of tension of 1.4V instead of 0.7V (simple diode) problematic if the tension to be rectified is weak.

Nonadjustable output voltage (= 1.41 X Veff - 1.4)

Points of currents if a condenser of filtering is used.

The output voltage will be then of 15.5V and not of 12V.

The bridge of Sauty consists of two resistances, two condensers, a generator of sinusoidal tension and a detector having a great impedance of entry. R_{1} and R_{2} are consisted a potentiometer whose cursor is connected to the detector, C1 is a condenser of known value and Cx are the condenser of unknown value. As the resistance of escape of the modern condensers is very large the impedance of a condenser is in practice Z = 1 ⁄ Cω. With the balance of the bridge, that is to say when (V_{A} - V_{B} ) = 0, one can write: Cx = Co.R_{2} ⁄ R_{1}

With the balance of a bridge, the products in cross of the impedances are equal. The optimal sensitivity of a bridge is obtained when the 4 impedances have close values. As the impedance of the condensers is high, it is necessary to use a potentiometer whose resistance is rather large.

The Wheatstone bridge is an measuring instrument invented by Samuel Hunter Christie in 1833, then improved and popularized by Charles Wheatstone in 1843. This is used to measure an unknown electrical resistance by balancing of two branches of a lattice network, with a branch containing the unknown component.

Let us consider the figure above. The bridge consists of two known resistances R_{1} and R_{2}, of a variable resistor of R_{3} precision and of a galvanometer V_{G}.

The potential at the junction point between R_{1} and R_{2} (noted D) is obtained thanks to the theorem of Millman and is worth U_{AC}.R_{2}/(R_{1} + R_{2}), where U_{AC} is the potential difference at the boundaries of the pile. If we place between R_{3} and the mass an unknown resistance, R_{x}, the tension at the junction point between R_{3} and R_{x} are worth U_{AC}.R_{x} ⁄ (R_{3} + R_{x}).

Let us adjust R_{3} in order to cancel the current in the galvanometer, the potential difference at the boundaries of this one is thus null. By equalizing the two tensions calculated above, one finds : R_{x} = R_{3} * R_{2} ⁄ R_{1}

In practice, the Wheatstone bridge comprises a whole of gauged resistances, in order to be able to measure a broad range of values of R_{x} with only one precision resistor, it is enough to change report ⁄ ratio R_{1} ⁄ R_{2}.

Use for the gauges of deformations

The Wheatstone bridge is also used at the time of the placement of gauges of deformation.

A gauge of deformation is based on the property which have certain materials to see their conductibility varying when they are subjected to constraints, pressures or deformations (piézorésistance) such known under the name of barrorécepteurs. It makes it possible to manufacture pressure pick-ups, acceleration, etc As the variations of resistance are too weak to be directly measurable, it is necessary to call upon an assembly in Wheatstone bridge.

Supplied with a source of tension the bridge has, with balance, a null tension U_{AC}, but the variation of one or the other of resistances reveals a nonnull tension. In practice, several of these resistances are gauges.

The interest of this assembly is that two adjacent resistances act as opposite direction and two opposite resistances act in the same direction. One can thus reduce the parasitic variations (like the temperature) and to have a better precision.

R_{x} = R_{b} * R_{c} ⁄ R_{a}

V_{b} = V_{in} * {(R_{x} ⁄ R_{x} + R_{c}) - (R_{b} ⁄ R_{b} + R_{a})}

V

A Maxwell Bridge is an electronic type of circuit derived from the Wheatstone bridge making it possible to measure the value of an unknown inductance thanks to a voltmeter or galvanometer of precise details, a resistance and a calibrated condenser.

That is to say the circuit opposite:

One seeks to be in the presence of the bridge known as "balanced" what occurs when the current circulating in the voltmeter ⁄ galvanometer is null. However U = Z * I, law of Ohm in alternative course. One thus seeks to return the tension measured to the voltmeter null.

The theorem of Millman gives when this tension is null (with Z is the complex impedance equivalent to R_{2} parallel in C_{2}):

R_{3} + j * L_{3} * ω = (R_{1} * R_{4} ⁄ Z) ⇔ R_{3} + j * L_{3} * ω = (R_{1} * R_{4}) * (1 ⁄ R_{2} + j * C_{2} * ω)

Maybe while equalizing left real and imaginary:

R_{3} = (R_{1} * R_{4} ⁄ R_{2}) and L_{3} = (R_{1} * R_{4}) * C_{2}

There is a result independent of the frequency of the generator

Maybe while equalizing left real and imaginary:

R

There is a result independent of the frequency of the generator

The diagram of the oscillator with bridge of Wien

The bridge of Wien, developped at the point by max Wien, is an electrical circuit made up of two impedances Z1 and Z2 in series. Z1 consists of a R1 resistance and a C1 condenser in series, Z2 of a R2 resistance and a C2 condenser in parallel.

Oscillator with bridge of Wien

It can also be used to produce a producing oscillator of the sinusoidal signals with a low distortion.

Let us recall that an oscillator is composed of two parts:

- an amplifier: this one has, according to the times, summer carried out with a vacuum tube, or with one or more bipolar transistors or with field effect nowadays, one can easily integrate an amplifier on a chip
- a circuit of reaction, placed between the exit of the amplifier and its entry, this circuit implements various impedances: resistances, condensers, reels, quartz.

It is the circuit of reaction which determines the frequency of oscillation. Indeed, this one occurs at a frequency where the condition of oscillation n.Go = 1 is satisfied. N and Go, both complexes, represent the profit of the circuit of reaction and the profit of the amplifier.

At the frequency ƒ = 1 ⁄ 2π √R_{1}R_{2}C_{1}C_{2}is ƒ = 1 ⁄ 2πRC, the profit of the filter of Wien is worth 1/3 and the output signal east in phase with the entry signal. By connecting the filter of Wien between the exit and the entry of an amplifier of profit 3 (an operational amplifier in the figure), one obtains an oscillator which produces a sinusoid at the frequency indicated.

In general, one takes R1 = R2 and C1 = C2.

Stabilization of the amplitude of the oscillations

The profit of the AOP depends on resistances R3 and R4 to have a profit of 3, one will take R3 = 2 R 4.

But the inaccuracies of the values of R3 and R4 make that this condition never is completely met. That it occurs then:

- if R3 <; 2 R 4, the oscillator does not oscillate
- if R3 > 2 R 4, the oscillation starts well, the amplitude grows up to the value limits, given by the supply voltage of the AOP, the problem, it is that under this condition the form of wave is distorted, the tops are flattened.

To cure this problem, one replaces R3 or R4 by a CTP or a CTN (resistances whose value grows or decrease with the temperature). The amplitude is stabilized with a value such as R3 is equal to 2 R 4.

That functions in the following way: let us suppose that R4 is a CTP. If, for an unspecified reason, the amplitude grows slightly, the power dissipated in R4 increases, which makes thus grow its value and reduced the profit of the AOP, which brings back the amplitude to its correct level.

Principle:

The bridge of Owen consists of a resistance fixes P of a condenser fixes C, of a variable resistor Rv in series with a variable capacitator Cv and finally of an unknown inductance modelled by a pure inductance Lx in series with a resistance X-ray.

To show that if the tension between the terminals of the detector is null one has the relations:

X-ray = PC ⁄ Cv (1)

Lx = P.C.Rv (2)

Lx = P.C.Rv (2)

It is impossible to balance this bridge uninterrupted. So the bridge is rather difficult to balance : it is necessary to proceed by gropings to find the value of Rv and that of Cv which give balance. In the program, one varies Cv by slipping a cursor simply. For a real assembly, it is necessary to handle a series of switches and the adjustment of this bridge is tiresome. The calculation of the literal value of the effective value of the terminal voltage of the detector being rather painful, I used a purely numerical calculation of this tension.

The practical realization of this assembly requires some care. For safety reasons the mass of the apparatuses is connected to the ground. If a traditional oscilloscope and generator BF are used, a terminal of the generator is connected on a terminal of the oscilloscope. It is necessary to use is a differential oscilloscope which makes it possible to isolate the terminals from entry of the mass is a generator BF with double insulation whose exits are isolated from the ground.

The bridge out of H is an electronic structure being used to control the polarity at the boundaries of a dipole. It is composed of four elements of commutation generally schematically laid out in the shape of H from where the name. The switches can be relays, transistors, or other elements of commutation according to the application concerned.

This structure is found in several applications of the electronics of power including the control of the engines, the converters and choppers, as well as the inverters. It is presented in various forms passing by the integrated circuits for the applications of low and average powers, the circuits discrete as well as the modules integrated for the averages and high powers.

Principle of operation

One uses the bridge by activating the switches of various combinations to obtain the desired connection. The following table summarizes the allowed combinations. All the combinations which do not appear in the table are prohibited and create a short-circuit of the source. The current of reference for the load is regarded as being from left to right.

S1 | S2 | S3 | S4 | Result |

X | X | X | X | No terminal voltage of the load. |

* | X | X | * | Positive current through the load. |

X | * | * | X | Negative current through the load. |

* | * | X | X | Charge shorted-circuit. |

X | X | * | * | Charge shorted-circuit. |

Use with the engines with D.C. current

Pont out of H with an active branch

Pont out of H with an active branch

The bridge out of H makes it possible to control the polarity of the terminal voltage of the engine, or to subject it to any tension (turned off engine). The switches are actuated two by two is S1-S4 or S2-S3 to make turn the engine in a direction or the other. The pairs of relay can have different powers according to whether the use does not require the same couple in a direction as in the other.

Moreover, the bridge out of H makes it possible to carry out a magnetic braking if it is able to dissipate the generated power of it. This operation is carried out while actuating is the two switches higher or lower at the same time, which shorts-circuit the terminals of the engine, and the fact consequently of slowing down. Better still, it is possible with a little electronics and a sophisticated controller to carry out a regenerative braking. In the case of a battery food, energy is returned to the batteries rather than dissipated in the switches of the bridge.

Use with the choppers and the inverters

The bridge out of H can be ordered with signals modulated in width of impulse. When such a signal is applied to one of the lower switches while the switch higher opposite is in conduction, the bridge becomes indeed a chopper making it possible to vary the average power transmitted to the load. In another type of application, the bridge can be commutated so as to vary the polarity of the charging voltage in way cyclic to make an inverter of it.

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