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Question Number 193065 by MikeH last updated on 03/Jun/23

Commented by MikeH last updated on 03/Jun/23

$$\mathrm{Find}{V}_{\mathrm{out}}\mathrm{from}\mathrm{the}\mathrm{circuit}\mathrm{above}.$$

Answered by aleks041103 last updated on 05/Jun/23

$$GoldenrulesforOpAmps:$$$$1)I_{in}=0$$$$2)V_{in+}=V_{in-}$$$$3)V_{+}>V_{-}\Rightarrow V_{out}=+V_c$$$$4)V_{+}<V_{-}\Rightarrow V_{out}=-V_c$$$$$$$$V_{+}=0=V_{-}=V_D$$$$\frac{V_{out}}{R_3}=I_{DC}$$$$(R_s+R_{11})I_{AB}+R_{12}(I_{AB}+I_{DC})=V_c$$$$R_{12}(I_{AB}+I_{DC})=-I_{DC}{R}_3$$$$\Rightarrow R_{12}{I}_{AB}=-(R_{12}+R_3)I_{DC}$$$$\Rightarrow I_{AB}=-\frac{R_{12}+R_3}{R_{12}{R}_3}{V}_{out}$$$$\Rightarrow (R_s+R_{11})(-\frac{R_{12}+R_3}{R_{12}{R}_3}{V}_{out})+R_{12}(-\frac{R_{12}+R_3}{R_{12}{R}_3}+\frac{1}{R_3})V_{out}=V_c$$$$-(\frac{(R_s+R_{11})(R_{12}+R_3)}{R_{12}{R}_3}+1)V_{out}=V_c$$$$\Rightarrow V_{out}=-\frac{1}{\frac{(R_s+R_{11})(R_{12}+R_3)}{R_{12}{R}_3}+1}{V}_c$$

Commented by aleks041103 last updated on 05/Jun/23

$$R_{11}istheresistancebetweenBandthecenter$$$$pinofthevaristor{R}_1$$$$R_{12}istheresistancebetweenCandthecenter$$$$pinofthevaristor{R}_1$$$$R_1=R_{11}+R_{12}$$

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