**What is the role of the differential amplifier circuit in increasing the input resistance?**
(a) emitter bias difference
(b) current source bias difference
A differential amplifier has two input terminals and two output terminals, allowing for both double-ended and single-ended signal configurations. In a double-ended input configuration, the signal is applied to both inputs simultaneously, while in a single-ended input setup, the signal is applied between one input and ground, with the other input grounded. Similarly, for outputs, a double-ended output takes the signal between the two outputs, whereas a single-ended output takes the signal from one output to ground. As a result, the differential amplifier can operate in four modes: double-ended input with double-ended output, single-ended input with double-ended output, double-ended input with single-ended output, and single-ended input with single-ended output. The examples provided earlier use the double-ended input and double-ended output configuration.
**Input Resistance Analysis of the Differential Amplifier Circuit**
*Figure 1: Classic differential circuit input resistance analysis*
Assuming ideal operational amplifier behavior and that all resistors are matched (R1 = R2 = R3 = R4 = 10 kΩ), we can analyze the input resistance seen at each terminal. Let RIN_V2 and RIN_V1 be the input resistances at the V2 and V1 terminals, respectively.
From Figure 1, the input resistance at the V2 terminal is straightforward:
RIN_V2 = R3 + R4 = 20 kΩ
For RIN_V1, we consider the current I flowing into the V1 terminal when a voltage V1 is applied. The input resistance can be expressed as RIN_V1 = V1 / I. Using the relationships from the circuit, we derive:
I = (V1 - VN) / R1
VN = VP = V2 * R4 / (R3 + R4)
Substituting these into the equation gives us:
RIN_V1 = V1 * (R3 + R4) * R1 / [V1(R3 + R4) - V2 R4]
Further simplification leads to:
RIN_V1 = [K1 * (R3 + R4) * R1] / [K1(R3 + R4) + K1 R4]
Where:
K1 = V2 - V1 (differential mode signal)
K2 = (V1 + V2) / 2 (common-mode signal)
If we assume the common-mode signal K2 is zero, then:
RIN_V1 = (R3 + R4) * R1 / (R3 + 2R4) = 6.666 kΩ
**Summary**
(1) The performance of an op-amp-based differential circuit depends on factors such as the op-amp's characteristics and resistor matching. These elements must be carefully considered during design.
(2) The input resistances at the two input terminals of the differential amplifier are often unequal, which can impact the overall performance of the circuit.
Due to these limitations, more advanced differential amplifiers and instrumentation amplifiers have been developed to provide better accuracy and stability in real-world applications.
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