AC voltage bridge

With an AC voltage bridge , also called an LCR measuring device , the inductance values of coils , capacitance values of capacitors and their losses as ohmic resistance can be measured in electrical measurement technology . ${\displaystyle L}$ ${\displaystyle C}$ ${\displaystyle R}$

In addition, AC voltage bridges are used for various other tasks, e.g. B. as a phase-rotating circuit .

Passive linear components under AC voltage

A real capacitor is approximately described by an (ideal) capacitance and an ohmic resistance , which are arranged in an equivalent circuit in parallel or in series . The same applies to the coil with inductance and ohmic resistance.

The components form complex resistances in an alternating current circuit . Their size can be specified by the amount and angle or by the real part and the imaginary part ${\displaystyle {\underline {Z}}}$ ${\displaystyle Z}$ ${\displaystyle \varphi }$ ${\displaystyle R}$ ${\displaystyle X}$

${\displaystyle {\underline {Z}}=Z\,\mathrm {e} ^{\mathrm {j} \varphi }=R+\mathrm {j} X\,.}$

When inductance is when capacitance is ${\displaystyle L}$ ${\displaystyle {\underline {Z}}=\mathrm {j} \omega L;}$ ${\displaystyle C}$ ${\displaystyle {\underline {Z}}={\frac {1}{\mathrm {j} \omega C}}\,.}$

Here stand for the angular frequency and for the frequency of the applied sinusoidal alternating voltage; stands for the imaginary unit with . ${\displaystyle \omega =2\pi f}$ ${\displaystyle f}$ ${\displaystyle \mathrm {j} }$ ${\displaystyle \mathrm {j} ^{2}=-1}$

Measuring circuits

Basic circuit of an AC voltage measuring bridge

Principle of the measuring bridge

The AC voltage bridge is constructed like a Wheatstone bridge , see the adjacent circuit diagram. It requires an alternating voltage source for the supply and a measuring device sensitive to alternating voltage to determine the bridge transverse voltage; the four resistances can be complex. The bridge is said to be balanced if the transverse voltage is equal to zero, although the amplitude of the supply voltage is greater than zero. In this case it is

${\displaystyle {\frac {{\underline {Z}}_{1}}{{\underline {Z}}_{2}}}={\frac {{\underline {Z}}_{3}}{{\underline {Z}}_{4}}}}$

or

${\displaystyle {\underline {Z}}_{1}\cdot {\underline {Z}}_{4}={\underline {Z}}_{2}\cdot {\underline {Z}}_{3}}$

To meet this complex matching condition, the

Amount condition and the ${\displaystyle Z_{1}\ Z_{4}=Z_{2}\ Z_{3}}$

Angle condition must be met. ${\displaystyle \varphi _{1}+\varphi _{4}=\varphi _{2}+\varphi _{3}}$

Whether a bridge can be adjusted at all can be seen from whether the angle condition can be met.

In the case of an adjusted bridge, the measured value is calculated so that the complex adjustment condition must be fulfilled in the real and imaginary part .

Two changeable components are required to set the adjustment. Depending on the circuit, there are frequency-independent and frequency-dependent solutions. In the case of the latter, the bridge transverse voltage cannot be brought to zero, but only to a minimum if the supply voltage contains harmonic components.

Among the many AC voltage measuring bridges that have been developed, two versions have proven particularly effective; they are described here.

Vienna bridge

The bridge named after Max Wien is suitable for measuring a capacitance. In the next circuit diagram, the generally lossy capacitor to be measured is at the position of and is shown here as in the parallel equivalent circuit diagram. ${\displaystyle {\underline {Z}}_{1}}$ ${\displaystyle {\underline {Z}}_{x}}$

AC voltage measuring bridge for measuring a capacitance

With the complex matching condition in the form

${\displaystyle {\frac {1}{{\underline {Z}}_{x}}}={\frac {{\underline {Z}}_{4}}{{\underline {Z}}_{3}}}\ {\frac {1}{{\underline {Z}}_{2}}}}$

and

${\displaystyle {\frac {1}{{\underline {Z}}_{x}}}={\frac {1}{R_{x}}}+\mathrm {j} \omega C_{x}\quad ;\quad {\underline {Z}}_{3}=R_{3}}$

and accordingly for and according to the circuit, one obtains ${\displaystyle {\underline {Z}}_{2}}$ ${\displaystyle {\underline {Z}}_{4}}$

${\displaystyle {\frac {1}{R_{x}}}+\mathrm {j} \omega C_{x}={\frac {R_{4}}{R_{3}}}\left({\frac {1}{R_{2p}}}+\mathrm {j} \omega C_{2p}\right)}$

Real part:

${\displaystyle {\frac {1}{R_{x}}}={\frac {R_{4}}{R_{3}}}{\frac {1}{R_{2p}}}\quad ;\quad R_{x}={\frac {R_{3}}{R_{4}}}R_{2p}}$

Imaginary part:

${\displaystyle \omega C_{x}={\frac {R_{4}}{R_{3}}}\omega C_{2p}\quad ;\quad C_{x}={\frac {R_{4}}{R_{3}}}C_{2p}}$

In the case of capacitors with a high quality or low loss, a very high value can take on, which is difficult to set. In the borderline case of an ideal capacitor . For measurements on such components, instead of the parallel connection, a series connection is used in the position of , in which the ohmic resistance assumes a small value, in the ideal borderline case . The mathematical treatment for this is more difficult and the result is frequency dependent. ${\displaystyle R_{2p}}$ ${\displaystyle R_{2p}\rightarrow \infty }$ ${\displaystyle {\underline {Z}}_{2}}$ ${\displaystyle R_{2r}}$ ${\displaystyle R_{2r}\rightarrow 0}$

AC voltage bridge for measuring capacitance with low loss

With the complex matching condition in the form

${\displaystyle {\frac {{\underline {Z}}_{2}}{{\underline {Z}}_{x}}}={\frac {{\underline {Z}}_{4}}{{\underline {Z}}_{3}}}}$

and ${\displaystyle {\underline {Z}}_{2}=R_{2r}+{\frac {1}{\mathrm {j} \omega C_{2r}}}}$

you get

${\displaystyle \left(R_{2r}+{\frac {1}{\mathrm {j} \omega C_{2r}}}\right)\left({\frac {1}{R_{x}}}+\mathrm {j} \omega C_{x}\right)={\frac {R_{4}}{R_{3}}}}$

Real part:

${\displaystyle {\frac {R_{2r}}{R_{x}}}+{\frac {C_{x}}{C_{2r}}}={\frac {R_{4}}{R_{3}}}}$

Imaginary part:

${\displaystyle \omega C_{x}R_{2r}={\frac {1}{\omega C_{2r}R_{x}}}\quad ;\quad \omega C_{2r}R_{2r}={\frac {1}{\omega C_{x}R_{x}}}}$

By eliminating , one obtains an equation for ${\displaystyle R_{x}}$ ${\displaystyle C_{x}}$

${\displaystyle {\frac {C_{x}}{C_{2r}}}\left(\omega ^{2}C_{2r}^{2}R_{2r}^{2}+1\right)={\frac {R_{4}}{R_{3}}}}$

A capacitance with a low loss is indicated in the parallel equivalent circuit by  . Then it will be ${\displaystyle R_{x}\gg {\frac {1}{\omega C_{x}}}}$

${\displaystyle \omega C_{2r}R_{2r}={\frac {1}{\omega C_{x}R_{x}}}\ll 1}$

and the equation for simplifies to ${\displaystyle C_{x}}$

${\displaystyle C_{x}={\frac {R_{4}}{R_{3}}}C_{2r}}$

In this approximate solution, there is no frequency dependency. It is different with the labeling of the loss. In this circuit the result is independent of the approximation

${\displaystyle R_{x}={\frac {1}{\omega ^{2}C_{x}C_{2r}R_{2r}}}}$

Maxwell Vienna Bridge

A circuit similar to the Wien bridge for measuring one inductance with a second inductance is the Maxwell bridge . However, this does not provide high-quality results because

1. no coils are available whose inductance is known with sufficient accuracy for comparison purposes,
2. Coils are more lossy due to their line resistances.

Both disadvantages are avoided in the Maxwell-Wien bridge, which uses a capacitor as a reference component. In the adjacent circuit diagram, the lossy coil to be measured is at the position of and is shown here in the series equivalent circuit diagram. ${\displaystyle {\underline {Z}}_{1}}$

AC voltage measuring bridge for measuring an inductance

With the complex matching condition in the form

${\displaystyle {\underline {Z}}_{x}={\frac {{\underline {Z}}_{2}\,{\underline {Z}}_{3}}{{\underline {Z}}_{4}}}}$

and

${\displaystyle {\underline {Z}}_{x}=R_{x}+\mathrm {j} \omega L_{x}}$

${\displaystyle {\underline {Z}}_{2}=R_{2}}$ etc. according to circuit

the inductance is obtained from the imaginary part of the adjustment condition

${\displaystyle L_{x}=R_{2}R_{3}C_{4}}$

and the ohmic loss resistance from the real part

${\displaystyle R_{x}={\frac {R_{2}R_{3}}{R_{4}}}}$

Display and comparison

In the case of a DC voltage-fed measuring bridge, e.g. B. Wheatstone bridge in the preferred embodiment, the transverse voltage is positive or negative; the sign indicates the direction in which the adjustment must be made in order to achieve the adjustment.

In the case of an alternating voltage supply, the usual rectification value or rms value formation for displaying an alternating voltage does not provide a change in sign and therefore no characteristic for direction. The remedy is the controlled rectification , which generates a positive sign for "too much" or a negative sign for "too little".

With a rectifier control voltage synchronous to the bridge supply voltage , the R adjustment is possible, with a control voltage offset by 90 ° to the supply voltage, the C adjustment. In bridges with manual adjustment, if the phase shift is between 0 ° and 90 °, the system changes several times between R adjustment and C adjustment and iteratively sets the display to minimal, ideally zero.

literature

• Rupert Patzelt, Herbert Schweinzer (ed.): Electrical measuring technology. 2nd edition, Springer Verlag GmbH, Vienna 1996, ISBN 978-3-211-82873-1 .
• Dierk Schröder: Power electronic circuits. Function, design and application. 3rd edition, Springer Verlag, Berlin-Heidelberg-New York 2012, ISBN 978-3-642-30103-2 .

See also

• Vienna Robinson Bridge
• Schering Bridge
• Bridge circuit

Web links

• Bridge circuit (BRÜ) (accessed on November 5, 2015)
• Bridge circuits (accessed November 5, 2015)