Wheatstone Bridges

• Wheatstone Bridge


  developed by Charles Wheatstone; measures unknown resistance values and used as a means of calibrating measuring instruments by the use of a long resistive slide wire
• Wheatstone bridge is nothing more than simple series-parallel arrangements of resistances connected between a voltage supply terminal and ground producing zero voltage difference between the two parallel branches when balanced
• Design of a Wheatstone Bridge


  has two input terminals and two output terminals consisting of four resistors configured in a diamond-like arrangement
• Balanced Wheatstone Bridge Analysis


  analyzed simply as two series strings in parallel; voltage drop occurs across the resistors because of the current flowing through it as defined by Ohm's Law
• In a balanced bridge, since the two resistors are in series, the same current flows through both of them. The current flowing through these two series is given as: V/Rt. The source voltage Vs is divided among the two series resistors in direct proportion to their resistances
• Principle of Voltage Division


  produces a potential divider circuit or voltage divider network
• Voltage at point C is the voltage drop across the lower resistor, R2. Voltage at point D is also the voltage drop across the lower resistor, R4.
• Unbalanced Network


  result of swapping the two resistors is that both sides or "arms" of the parallel network are different as they produce different voltage drops
• Principle of the Wheatstone Bridge Circuit


  the resistance ratio of two parallel arms, ACB and ADB, results in a voltage difference between 0 volts (balanced) and the max supply voltage (unbalanced)
• Other uses for the Wheatstone Bridge


  to compare an unknown resistance Rx with others of known value
• Replacing R4 with a resistance of known or unknown value in the sensing arm of the Wheatstone Bridge corresponding to Rx and adjusting the opposing resistor, R3 to "balance" the bridge network, will result in a zero voltage output
• When does balance occur in a Wheatstone Bridge?


  R1/R2 = R3/Rx = 1
• Value of unknown resistance, Rx, at balance:


  Vout = (Vc - Vd) = (Vr2 - Vr4) = 0

  Rc = R2 / R1 +R2 and Rd = R4 / R3 + R4
• Balanced vs. Unbalanced


  balanced: voltage across output terminals is 0 volts

  unbalanced: output voltage either positive or negative depending on direction of unbalance