Linear Opamp Circuits

Study Unit 7: Linear Opamp Circuits - Basic Building Blocks and Instrumentation Amplifiers

Lecture Outcomes

• Topics include basic building blocks, summing amplifier, difference amplifier, negative resistance converter, and instrumentation amplifiers (IA).
• Discussion covers 3 opamp IA, voltage offsetting, and 2 opamp IA.

Basic Building Blocks

Summing Amplifier

• Circuit configuration includes an opamp with resistors R1, R2, R3 connected to the inverting input, and a feedback resistor RF connecting the output to the inverting input. Voltages v1, v2, v3 are applied to the resistors R1, R2, R3 respectively.
• The summing currents equation is i1 + i2 + i3 = iF, which leads to the output voltage equation: v{out} = -\left( \frac{RF}{R1} v1 + \frac{RF}{R2} v2 + \frac{RF}{R3} v3 \right).
• If R1 = R2 = R3 = R, the equation simplifies to v{out} = -\frac{RF}{R} (v1 + v2 + v3).

Difference Amplifier

• Circuit includes resistors R1, R2, R3, R4. Voltage v1 is connected to a network of R1 and R2, and voltage v2 is connected to a network of R3 and R4.
• The design equation for the output voltage is v{out} = \frac{R2}{R1} \left( \frac{1 + R1/R2}{1 + R3/R4} v2 - v_1 \right).
• Simplified approach: If \frac{R3}{R4} = \frac{R1}{R2}, then v{out} = \frac{R2}{R1} (v2 - v_1).

Negative Impedance/Resistance Converter (NRC)

• Normal resistor: Applying a test source results in R_{eq} = R.
• Negative Resistor Converter (NRC): Circuit diagram includes resistors R1 and R2 connected to an opamp.
• Analysis: Since iT = iR due to opamp action, the current iT is given by iT = \frac{vT - v{out}}{R} = \frac{vT - (1 + \frac{R2}{R1})vT}{R} = -\frac{R2}{R1} \frac{v_T}{R}.
• The equivalent resistance from the test source is found by solving for the ratio: R{eq} = \frac{vT}{iT} = \frac{vT}{-\frac{R2}{R1} \frac{vT}{R}} = -R \frac{R1}{R_2}.

Instrumentation Amplifier (Basic 3 Opamp)

• The circuit consists of three opamps (OP1, OP2, OP3) and resistors. Voltages v1 and v2 are inputs to OP1 and OP2 respectively.
• The input section gives: v{01} - v{02} = \left(1 + \frac{2R3}{RG} \right) (v1 - v2).
• The difference amplifier section gives: v{out} = \frac{R2}{R1} (v{02} - v_{01}).
• The overall design equation is: v{out} = A (v2 - v1), where the gain A = A1 A2 = \left(1 + \frac{2R3}{RG} \right) \left(\frac{R2}{R_1} \right).

Instrumentation Amplifier (Basic 3 Opamp with VREF offset)

• Similar to the basic 3 opamp IA but with an additional opamp (OP4) to introduce a voltage reference (VREF).
• The design equation is: v{out} = A (v2 - v1) + V{REF}. The VREF design is flexible, such as a buffered voltage divider.

Instrumentation Amplifier (Basic 2 Opamp)

• Circuit includes two opamps (OP1, OP2) and several resistors with an optional resistor R_G for adjustable gain.
• The design equation is: v{out} = \left(1 + \frac{R2}{R1} \right) \left( v2 - \frac{1 + R3/R4}{1 + R1/R2} v_1 \right).
• Simplified approach: If \frac{R3}{R4} = \frac{R1}{R2}, the output voltage simplifies to v{out} = \left( 1 + \frac{R2}{R1} + \frac{2R2}{RG} \right) (v2 - v_1).