The acid/alkaline balance of a fluid is measured by the \(\mathrm{pH}\) scale. The scale runs from \(\mathrm{o}\) (extremely acid) to 14 (extremely alkaline), with \(\mathrm{pH} 7\) being neutral. A pH electrode is a sensor that produces a small voltage that is directly proportional to the \(\mathrm{pH}\) of the fluid in a test chamber. For a certain \(\mathrm{pH}\) electrode, the proportionality factor is \(50 \mathrm{mV} / \mathrm{pH}\). A preamplifier is needed to interface this sensor with a variety of laboratory instruments. The output of the preamp must be \(1 \mathrm{~V}\) when the sensor is immersed in a test solution with \(\mathrm{pH}=4\) and 1.75 \(\mathrm{V}\) when it is immersed in a solution with \(\mathrm{pH}=7\). Design an amplifier to meet these requirements.

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At a pH of 4, the sensor produces (4 pH)(50 mV/pH) = 200 mV, and at the output of the interface it should produce 1 V. At a pH of 7, the sensor produces (7 pH) (50 mV/pH) = 350 mV, and at the output of the interface it should produce 1.75 V. Compute the required gain. Compute the bias voltage. K = VO (P1) - VO(P2) UTR (P1) - UTR (P2) KUTR + Vb = Vo (5)(200 mV) + V = 1V Vb =0 V The required gain is K = 5 and the bias voltage is V = 0 V. Since there is no bias voltage, use a noninverting amplifier to create an interface with a gain of 5 by selecting R = 4k and R = 1 k. The input to the interface is UTR. The design is shown below. Other designs are possible. VTR O 1V - 1.75 V 200 mV - 350 mV + www 4 1 kn o Vo