Common-collector (emitter follower) input resistance: in small-signal AC analysis, and assuming the emitter resistor RE represents the load seen at the emitter, the input resistance seen at the base (Rin, looking into the amplifier) is approximately given by which expression?

Introduction / Context:
The common-collector amplifier (also called an emitter follower) is prized for its high input resistance and low output resistance. Designers often use it as a buffer stage between a signal source and a load. This question asks you to recall the approximate analytical expression for the input resistance seen at the base, Rin, in terms of the emitter resistor RE and the transistor's current gain parameters. Getting this right helps you predict loading on the previous stage and avoid signal attenuation.

Given Data / Assumptions:

• Small-signal, linear AC operation around a bias point.
• RE is the effective AC emitter resistance (it may be RE || load seen at the emitter).
• beta denotes the small-signal current gain (ic/ib). alpha ≈ beta/(beta + 1).
• Bias network and source resistance effects are not dominating (first-order estimate).

Concept / Approach:
The emitter follower translates base current changes into much larger collector and emitter current changes. Looking into the base, the emitter resistor is “magnified” by approximately (beta + 1). Intuitively, a small base current perturbation produces (beta + 1) times larger emitter current, so the base sees a resistance that is (beta + 1) times the emitter-side resistance. A more complete model includes the intrinsic emitter resistance re and any loading at the emitter as RE_eff = RE || R_load || re, but the leading behavior is the (beta + 1) multiplication of whatever load is present at the emitter node.

Step-by-Step Solution:

Verification / Alternative check:
Use hybrid-pi or T-equivalent models. The base sees r_pi in series with a dependent source arrangement; transforming to the emitter side shows the (beta + 1) scaling of resistances reflected to the base. Spice simulations of an emitter follower corroborate that measuring input current into the base and dividing the applied small AC signal yields approximately (beta + 1) * RE as long as the transistor remains in its linear region.

Why Other Options Are Wrong:
Rin ≈ RE / (beta + 1): inverted dependence; it would predict lower input resistance for higher beta, which contradicts emitter-follower behavior.
Rin = RE * alpha: alpha is slightly less than 1 and does not capture the large multiplication effect; it severely underestimates Rin.
Rin ≈ RC / beta: RC is not the determining resistor in a common-collector stage; the collector is at AC ground in many implementations.
Rin independent of beta and RE: incorrect because both parameters strongly influence Rin.

Common Pitfalls:
Forgetting to include the load at the emitter (RE || R_load); neglecting the effect of bias network resistors which can shunt Rin; assuming Rin is infinite; or confusing common-emitter and common-collector formulas.

Final Answer:
Rin ≈ (beta + 1) * RE