De Sauty Bridge Construction Circuit and Theory

De Sauty Bridge is a very simple type of AC Bridge used to measure capacitance. Here we measure in unknown capacitance in terms of known capacitance and known resistance. Hence, we design a De Sauty Bridge by using two known resistances (R1 and R4), one known capacitance (C2) and one unknown capacitance (C3). The device gives the expression of C3 in terms of R1, R4, and C2.

Construction of De Sauty Bridge

For showing the basic construction of a De Sauty Bridge let us draw the circuit diagram of such bridge.

De Sauty Bridge
De Sauty Bridge

The first arm that is arm AB consists of a pure resistance R1. The second arm that is arm BC consists of a capacitor of unknown capacitance C2. Then the third arm that is arm CD consists of a standard capacitor of known capacitance C3. Forth arm that is BA consists of a pure resistance R4.

Theory of De Sauty Bridge

Now let us compare this De Sauty Bridge circuit with a generalized AC Bridge circuit. For that, we will draw a generalized AC Bridge circuit.

AC Bridge
AC Bridge

By comparing the De Sauty Bridge circuit and the AC Bridge circuit, we can write.

Now we know that the balanced condition of the AC Bridge circuit is

On comparison of this equation, we write

Now, if the value of resistance are equal, then

De Sauty Bridge has maximum sensitivity when the value of known capacitance and unknown capacitance are equal.

We cannot obtain perfect balancing in this type of bridge if the capacitors suffer from dielectric losses. So we can only obtain the perfect balancing if we use air condensers as the capacitors for the purpose.

There is another approach to create the equation for balancing the bridge. Let us explain that. Suppose the current flowing through the path ABC if i1. And the Current flowing through the path ADC is i2.

De Sauty Bridge Circuit
De Sauty Bridge Circuit

So, the voltage of node B in respect of node A is

Similarly, the voltage of node D in respect of node A is

At balanced condition there should not be any potential difference between node B and node D. Hence, we can write,

Again, the voltage of node B in respect of node C is

Similarly, the voltage of node D in respect of node C is

As we told in the previous lines that, the voltage of node B is the same as that of node D. Now we can write,

By dividing equation (i) by (ii), we get

This is the same expression of unknown capacitance which we have already derived in the previous section of this De Sauty Bridge article.

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