# Bridge circuit and the error caused by a differential amplifier

I am currently struggeling with solving the following problem: The circuit below shows a bridge circuit, where the differential voltage between the branches is measured by a differential amplifier. I need to know the relative systematic error caused by using the amplifier circuit.

Given values: $$R_0=100\Omega \\ \Delta R=1\Omega \\ R=1k\Omega$$

Well, my approach to solve this was to first analyze the bridge circuit itself, then together with the differential amplifier and calculate the relative error by:

$$\frac{\Delta V_a}{V_a}=\frac{V_{a-amp} - V_{a-ideal}}{V_{a-ideal}}$$

Analyzing the bridge circuit alone: $$V_D=V_2-V_1=V_s(\frac{R_0-\Delta R}{R_0+\Delta R +R_0-\Delta R}-\frac{R_0}{2R_0})=V_s(\frac{R_0-\Delta R}{2R_0}-\frac{1}{2})$$

Alright, now analyzing the complete circuit. Well, V_2 is now also applied on the two resistors R, located at the non-inverting input:

$$V_2=V_s\frac{(R_0-\Delta R) || 2R}{R_0+\Delta R + (R_0-\Delta R) || 2R}$$

But now I am stuck. What do I do with V_1? Because there is actually no ground in the upper branch of the differential amplifier (inverting input). Is my approach as it is correct and my calculations up until now?

• $V1=V_S\frac{R_0}{2R_0}$ but your input resistance is to low 1k (IMO) it will affect the bridge. – Marko Buršič May 14 '16 at 14:53
• Have you heard about virtual ground? The inverting input has ground potential, so 1k is parallel on the lower R0. – Marko Buršič May 14 '16 at 14:57
• Yeah but this voltage divider is only valid if its unloaded. But with the differential amplifier it is loaded and, as you said, it will be affected due to the low 1k resistors, but how do I express that in equations so I can calculate a relative error? – Daiz May 14 '16 at 14:58
• Why does the inverting input has ground potential? The non-inverting input is not directly on ground, but on some voltage V+, so V+ is also "created" at the inverting input. At least thats how I understand it. Am I wrong? – Daiz May 14 '16 at 15:00
• What do you mean by "systematic error"? I would worry about common mode voltage suppression. It causes troubles with bridge measurements. Is it what you mean? – Master May 14 '16 at 15:04