Discussion
Which topology converts a voltage into a current?
Answer: A
Current series feedback raises both impedances: high at the input so it senses a voltage without loading, and high at the output so it delivers a current independent of load. That is a transconductance amplifier, and an emitter resistor left unbypassed is its commonest form. The four topologies cover the four possible input-output conversions exactly, which is why there are neither more nor fewer of them.
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