Circuits I · Ideal operational-amplifier circuits
An ideal operational amplifier with supplies ±15.0 V (saturation at the rails) is…
Problem
An ideal operational amplifier with supplies \(\pm15.0\,\mathrm{V}\) (saturation at the rails) is connected as a four-resistor difference amplifier. Resistor \(R_1=25.0\,\mathrm{k}\Omega\) is connected from source \(v_1\) to the inverting input, and \(R_f=75.0\,\mathrm{k}\Omega\) is connected from the output to the inverting input. Resistor \(R_2=25.0\,\mathrm{k}\Omega\) is connected from source \(v_2\) to the noninverting input, and \(R_g=75.0\,\mathrm{k}\Omega\) is connected from the noninverting input to ground. The DC values are \(v_1=4.20\,\mathrm{V}\) and \(v_2=4.50\,\mathrm{V}\). There is no additional load. In the linear region, \(i_+=i_-=0\) and \(v_+=v_-\). Determine (a) \(v_+\) and \(v_-\), (b) \(v_o\), (c) the currents in \(R_1\) and \(R_2\), and (d) whether the output is inside the supply limits. Also report the differential gain \((v_2-v_1)\mapsto v_o\) implied by the matched resistor ratios.
Hint
Matched ratios \(R_f/R_1=R_g/R_2\) reduce the circuit to \(v_o=(R_f/R_1)(v_2-v_1)\).
Check your work
Work the problem yourself first. Then open it in Training to check your answer and read the full worked solution.
The answer check and full solution for this problem come with ProofAnvil Practice membership ($19 USD monthly). See membership. Or start with the free Circuits I sample problem: Try the free sample problem.
More Circuits I practice problems
- A charge q=50 μC is moved slowly from node n to node pVoltage, current, power, and resistive networks
- A connected resistive network has three essential nodes labelled A, B, and NVoltage, current, power, and resistive networks
- A network has essential nodes A, B, C, and reference node NNode, mesh, superposition, and equivalent circuits
- A connected planar circuit occupies two adjacent rectangular windows whose shared…Node, mesh, superposition, and equivalent circuits
- A linear one-port has terminals t and the reference node (ground)Ideal operational-amplifier circuits
- Capacitors C_1=20 μF and C_2=30 μF are connected in seriesCapacitors, inductors, and first-order transients
- A 40 μF capacitor is connected, for all t<0 and for a duration sufficient to reach DC…Capacitors, inductors, and first-order transients
- A source-free parallel circuit consists of R = 8 Ω, L = 2 H, and C = 1/32 FSecond-order natural and step responses
- A three-phase source is balanced and positive-sequencePhasors, sinusoidal steady state, and AC power