COMMON-COLLECTOR AMPLIFIER SMALL-SIGNAL VOLTAGE GAIN INPUT AND OUTPUT IMPEDANCES SMALL-SIGNAL CURRENT GAIN

C-C Amplifier Collector connected directly to Vcc Output signal taken at emitter with respect to ground Emitter-follower circuit

Small-signal equivalent circuit of emitter-follower Vcc or collector terminal is at signal ground. o/p resistance, ro parallel with dependent current source.

Another small-signal equivalent circuit of emitter follower Assume Cc is short-circuited. ro parallel with dependent current source and collector terminal is at ground. Rearrange the previous cct so that all signal grounds connected are at same point, we will get..

C-C Amplifier equations We see that Output voltage is written as Apply KVL around base-emitter loop Or We can also write Where Combine all above equations, the small-signal voltage gain is:

Input impedance Input resistance looking into the base, Rib is given by: Since Ie is (1+β) times Ib, the effective impedance in emitter is multiplied by (1+β). This multiplication is known as resistance reflection rule. Input resistance at the base, Rib is: rπ + [effective resistance in emitter x (1+β)]

Output resistance To find o/p resistance, assume input signal source, Vs is ideal and Rs=non-zero. Refer to below figure, we can determine o/p resistance looking back into o/p terminals. Set independent voltage source, Vs=0 (short circuit).

Output resistance A test voltage, Vx is applied to o/p terminal and produce test current, Ix. The control voltage, Vπ is not zero, but is a function of test voltage. The output resistance, Ro is given by: Summing current at the o/p node, we have: Control voltage in term of test voltage using voltage divider:

Output resistance Substitute the above eq and rearrange leads to: Note that, gmrπ=β, we find that: Or

Things to remember.. DEPENDENT SOURCE IS A SOURCE WHICH CAN ONLY GENERATE SIGNALS IF THERE IS ANOTHER SOURCE GIVING A SIGNAL INDEPENDENT SOURCE GENERATES ITS OWN SIGNAL

Small-signal equivalent circuit - small-signal current gain

Small-signal current gain, Ai Determine current gain using input resistance and concept of current divider. Small-signal current gain is defined as: Using current divider, we write base current in term of input current:

Small-signal current gain Since gmVπ=βIb, then Write Ie in term of Io produces Combine all equations yield to: If R1||R2 >> Rib and ro>>RE, then Current gain >> 1 (unity). Voltage gain < 1. Thus, C-C circuit produces small-signal power gain

COMMON-BASE AMPLIFIER SMALL-SIGNAL VOLTAGE GAIN INPUT AND OUTPUT IMPEDANCES SMALL-SIGNAL CURRENT GAIN

Common-base circuit Use hybrid-π equivalent circuit. Dc analysis is the same as C-E circuit. Base is at signal ground and input signal is applied to emitter. The output signal is measured at collector terminal. Assume load is connected to output through coupling capacitor, Cc2.

C-B Small-signal equivalent circuit Hybrid-π model for npn transistor with ro=∞ Small-signal equivalent circuit for C-B

Small-signal voltage gain, Av Rearrange previous 2 equations, small-signal voltage gain is: As Rs  0, voltage gain becomes: Output voltage is given by: Apply KCL at emitter node, Since β=gmrπ, above eq. can be written as: Then,

Small-signal current gain, Ai Ai = Io / Ii . Apply KCL at emitter node, Solving for Vπ, we obtain: The load current is: Combine all above equations, small-signal current gain is: If RE ∞ and RL 0, current gain equation becomes For C-B circuit, voltage gain >> 1 and current gain < 1. So, we get small power gain. Application of C-B cct take advantage of i/p and o/p resistance characteristic.

C-B Input impedance Rie Small-signal equivalent cct looking into emitter. The control voltage reverse the direction of dependent current source. The input resistance looking into the emitter is: + V - r Rie gmV RC RL Ii

Input impedance Apply KCL at the input, Thus, The resistance looking into the emitter with base grounded -> re and is quite small. When input signal is a current source, a small input resistance is desirable.

Output impedance Ro C-B circuit for output resistance calculations - V + r Ro gmV RC amplifier RS RE Vx Ix E

Output impedance Independent source, vs set = 0. KCL equation at the emitter, Since vs =0, Vπ=0 and so do gmVπ = 0. The output resistance looking into the o/p terminals is:

Comparison Voltage gain Current gain Input resistance Configuration Voltage gain Current gain Input resistance Output resistance Common emitter Av > 1 Ai > 1 Moderate Moderate to high Emitter follower Av ≈ 1 High Low Common base Ai ≈ 1