impedance matching for the amplifier stage

In which configuration BJT is used for impedance matching and why?

Not sure I understand the question. Are you asking how to impedance match for a BJT amplifier?

Is this a homework question?

I presume that you are asking about impedance matching in RF amplifiers.

BJT "used for" impedance matching sounds inappropriate. In most cases i would talk about BJT "involved in" impedance matching. It applies to all configurations that are used for amplifiers, mainly common emitter and common base.

Hi GBHT !
It is enough that you know that reflected impedance from base to the emitter is re which will given by hie/hfe =========> hie=26mv/ib thus if you change the ib the reflected impedance will have change as your desired value . but it won't be used at high powers .
Best Wishes
Goldsmith

If you examine the output impedance of complementary CMOS and 50 Ohm line drivers you will find a similarity in structure but the crossover distortion is reduced by having a current surge during crossover which tends to make dynamic power consumption increase with transition frequency. THis used exclusively for driving square waves or pulses, where harmonic content is inherent in the signal and distortion is less important.

When it comes to RF amplifiers, the return loss from impedance mismatch and harmonic & IM distortion are significantly more important than the efficiency of complementary outputs. Emitter followers can be designed to have much lower impedance than required and then a series resistor is added to match the desired impedance of the transmission line but these also have issues with spurious resonance from capacitive loads and degenerative feedback.

Hence for RF amplifiers they tend to be inefficient common emitter (class A) and common base which use the collector resistance to determine the gain and the output impedance for matching with subsequent stages. The same configuration is true for FET and MOSFETs which typically use GaAs rather than Silicon to get much higher gain bandwidth products for RF but a much greater cost. Some have improved Germanium for RF applications.

In many cases, Strip and transformers are used for impedance matching as well.
Even in the old days were used for audio speaker impedance matching. https://en.wikipedia.org/wiki/File:Tube_push_pull_poweramplifier.PNG

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If you choose to learn about RF amplifiers which need much more than simple impedance matching, you need to become familiar with the terminology.

http://www.minicircuits.com/app/AN60-038.pdf