Bridge networks

BRIDGE NETWORKS

1. DC BRIDGE NETWORKS

The DC bridge is an electrical circuit for the precise measurement of resistances. The best known bridge circuit is the Wheatstone bridge, named after Sir Charles Wheatstone (1802 – 1875), an English physicist and inventor.

The Wheatstone bridge circuit is shown in the figure below. The interesting feature of this circuit is that if the proyducts of the opposite resistances (R1R4 and R2R3) are equal, the current and voltage of the middle branch is zero, and we say that the bridge is balanced. If three of the four resistors (R1, R2, R3, R4) are known, we can determine the resistance of the fourth resistor. In practice the three calibrated resistors are adjusted until the voltmeter or ammeter in the middle branch reads zero.

Wheatstone bridges

Let’s prove the condition of balance.

When in balance, the voltages on R1 and R3 must be equal:

therefore

R₁R₃+R₁ R₄ = R₁ R₃ + R₂ R₃

Since the term R₁ R₃ appears on both sides of the equation, it can be subtracted and we get the condition of balance:

R₁ R₄ = R₂ R₃

In TINA you can simulate balancing the bridge by assigning hotkeys to the components to be changed. To do this, double click on a component and assign a hotkey. Use a function key with the arrows or a capital letter, e.g. A to increase and another letter, e.g. S to decrease the value and an increment of say 1. Now when the program is in interactive mode, (the DC button is pressed) you can change the values of the components with their corresponding hotkeys. You can also double-click on any component and use the arrows on the right side of the dialog below to change the value.

Example

Find the value of R_x if the Wheatstone-bridge is balanced. R₁ = 5 ohm, R₂ = 8 ohm,

R₃ = 10 ohm.

The rule for R_x

Checking with TINA:

Click here to load or save this circuit

If you have loaded this circuit file, press the DC button and hit the A key a few times to balance the bridge and see the corresponding values.

2. AC BRIDGE NETWORKS

The same technique can also be used for AC circuits, simply by using impedances instead of resistances:

In this case, when

Z₁Z₄ = Z₂ Z₃

the bridge will be balanced.

If the bridge is balanced and for example Z_1,Z₂ , Z₃are known

Z₄ = Z₂ Z₃ / Z₁

Using an AC bridge, you can measure not only impedance, but also resistance, capacitance, inductance, and even frequency.

Since equations containing complex quantities mean two real equations (for the absolute values and phases or real and imaginary parts) balancing an AC circuit normally needs two operating buttons but also two quantities can be simultaneously found by balancing an AC bridge. Interestingly the balance condition of many AC bridges are independent of the frequency. In the following we will introduce the most well known bridges, each named after their inventor(s).

Schering – bridge: measuring capacitors with series loss.

Find C so that the ammeter reads zero in the Schering-bridge. f = 1 kHz.

The bridge will be balanced if:

Z₁Z₄ = Z₂ Z₃

In our case:

after multiplication:

The equation will be satisfied if both real and imaginary parts are equal.

In our the bridge, only C and R_x are unknown. To find them we have to change different elements of the bridge. The best solution is to change R₄ and C₄ for fine-tuning, and R₂ and C₃ to set the measurement range.

Numerically in our case: