Balanced Bridge Circuit

The Balanced Bridge Circuit

PART 1

Bridges and Voltage Dividers: In Experiment 1, we looked at one of the simplest useful circuits - the voltage divider. In many simple applications of electronics, we have only a small number of standard voltages in whatever circuits we are building. When we use a 9V battery as our source we have only one voltage level available, unless we use a voltage divider to get smaller voltages. We can also use a divider, as pictured in Figure A-1, to measure resistance, if we have some device with an unknown resistance. For example, if we connect an unknown resistor in series with a known resistor, then the voltage across the unknown resistor can tell us the value of the resistance. An even better measurement can be done by combining two voltage dividers in a configuration like the one shown in the following figure. Note that if R1 = R2 = R3 = R4, the voltages at the two points marked Vleft and Vright will be equal to half of the source voltage. Thus, their difference should be zero. Whenever the voltage difference across a bridge is zero, we say that the bridge is balanced.

Figure A-1.

The following equations apply to the bridge circuit. When dV = 0, the bridge is balanced:

Modeling a bridge in PSpice

In this part, we will set up a bridge in PSpice and look at the effect of a small change in one of the resistors on the difference across the bridge.

A.1 Look at the behavior of a balanced bridge circuit.

Set up the circuit on the previous page as shown.

Use a 9V amplitude, 1kHz frequency and no DC offset.

Place voltage markers at Vleft and Vright, or use the “voltage difference markers.” Then run a transient analysis. (You have done enough transients now to be able to find a reasonable “run to time” and “step size”.)

Add a Trace of the difference between the two voltages, (Vleft - Vright). (It will already be there if you used the “voltage difference markers.”)

Is the difference zero?

A.2 Look at the behavior of an unbalanced bridge circuit.

Now, change R4 to be equal to 362O, a 2% change in R.

Do the analysis again and add the trace of the difference between the two voltages.

What is the amplitude of the difference voltage as a percentage of the source voltage?

Label the plot, print it and include it with your report.

A.3 Analyze this circuit by hand

Use voltage dividers to find the voltages at the two points and their difference. Make sure that your answer agrees with the PSpice simulation.

Assume that R1 = R2 = R3 are known resistors equal to R, and that R4 is unknown. Derive a formula for R4 in terms of R , the source voltage V1, and the voltage difference between the two divider voltages (dV=Vleft-Vright). [Hint: Substitute voltage divider expressions in for Vleft and Vright and solve for R4.]

A.4 Parameter sweep

In PSpice, it is possible to run simulations for several values of ...