9/2/2018

Indian Institute of Technology Jodhpur, Year 2018

Analog (Course Code: EE314) Lecture 11‐12: BJT

Course Instructor: Shree Prakash Tiwari Email: [email protected]

Webpage: http://home.iitj.ac.in/~sptiwari/ Course related documents will be uploaded on http://home.iitj.ac.in/~sptiwari/EE314/

Note: The information provided in the slides are taken form text books for microelectronics (including Sedra & Smith, B. Razavi), and various other resources from internet, for teaching/academic use only 1

Common‐Emitter (CE) Topology

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Small Signal of CE

vout Av  vin

Limitation on CE Voltage

• Since gm = IC/VT, the CE voltage gain can be written as a function of VRC , where VRC = VCC ‐ VCE. • VCE should be larger than VBE for the BJT to be operating in active mode.

IC RC VRC Av   VT VT

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Voltage‐Gain / Headroom Tradeoff

I/O Impedances of CE Stage

• When measuring output impedance, the input port

has to be grounded so that vin = 0.

vX vX Rin   r Rout   RC iX iX

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CE Stage Design Trade‐offs

Inclusion of the Early Effect

• The Early effect results in reduced voltage gain of the CE amplifier.

Av  gm(RC ||rO )

Rout  RC ||rO

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Intrinsic Gain

• As RC goes to infinity, the voltage gain approaches its maximum possible value, gm × rO, which is referred to as the intrinsic gain. • The intrinsic gain is independent of the bias current:

Av   g m rO

V A Av  VT

Current Gain, AI • The current gain is defined as the ratio of current delivered to the load to current flowing into the input. • For a CE stage, it is equal to .

iout AI  iin

AI CE  

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Emitter Degeneration • By inserting a in series with the emitter, we “degenerate” the CE stage. • This topology will decrease the gain of the amplifier but improve other aspects, such as linearity, and .

Small‐Signal Analysis

• The gain of a degenerated CE stage = the total load

resistance seen at the collector divided by 1/gm plus the total resistance pldlaced in series with the emitter.  g R  R A  m C  C v 1 1 g m RE  RE g m

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Small‐Signal Analysis

• The gain of a degenerated CE stage = the total load

resistance seen at the collector divided by 1/gm plus the total resistance pldlaced in series with the emitter.  g R  R A  m C  C v 1 1 g m RE  RE g m

Emitter Degeneration Example 1

Note that the input impedance of Q2 is in parallel with RE. R A  C v 1 RE ||r2 gm1

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Emitter Degeneration Example 2

Note that the input impedance of Q2 is in parallel with RC. R || r A   C  2 v 1  RE g m1

Input Impedance of Degenerated CE Stage

• With emitter degeneration, the input impedance is

increased from r to r + (+1)RE ― a desirable effect.

(VA  )

vx  rix  RE (1 )ix

vx Rin   r ( 1)RE ix

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Output Impedance of Degenerated CE Stage

• Emitter degeneration does not alter the output impedance, if the Early effect is negligible.

(VA  )  v     vin  0  v   gmv RE  v  0  r 

vx Rout   RC ix

Degenerated CE Stage as a “Black Box”

(VA  )

vin iout  gm 1 1 (r  gm )RE i g G  out  m m • If gmRE >> 1, Gm is more linear. vin 1 gm RE

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Degenerated CE Stage with Base Resistance

(VA  ) v v v out  A . out vin vin v A v  R out  C vin r  ( 1)RE  RB

 RC Av  1 RB  RE  g m  1

Degenerated CE Stage: Input/Output Impedances

• Rin1 is more important in practice, because RB is often the output impedance of the previous stage.

(VA  )

Rin1  r  ( 1)RE

Rin2  RB  r  ( 1)RE

Rout  RC

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Emitter Degeneration Example

Emitter Degeneration Example

(RC || R1) Av  1 RB  R2  gm  1

Rin r ( 1)R2

Rout  RC || R1

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Output Impedance of Degenerated CE Stage

with VA<∞ • Emitter degeneration boosts the output impedance. – This improves the gain of the amplifier and makes the circuit a better .

Output Impedance of Degenerated CE Stage

with VA<∞ • Emitter degeneration boosts the output impedance. – This improves the gain of the amplifier and makes the circuit a better current source.

R out  1  g m ( R E || r )rO  R E || r

R out  rO  ( g m rO  1)( R E || r )

R out  rO 1  g m ( R E || r )

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Two Special Cases

Stage with explicit depiction of ro:

1) RE  r : Rout  rO (1 gmr )  rO

2) RE  r : Rout  (1 gm RE )rO

Analysis by Inspection • This seemingly complicated circuit can be greatly simplified by first recognizing that the capacitor creates an AC short to gg,round, and gygradually transforming the circuit to a known topology.

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Analysis by Inspection • This seemingly complicated circuit can be greatly simplified by first recognizing that the capacitor creates an AC short to gg,round, and gygradually transforming the circuit to a known topology.

Rout  R1 || Rout1 Rout1  1 g m (R2 || r )rO Rout  1 g m (R2 || r )rO || R1

Example: Degeneration by Another BJT

Rout  1 gm1(rO2 || r1)rO1

• Called a “”, this circuit offers many advantages that we will study later...

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Bad Input Connection

• Since the microphone has a very low resistance

(connecting the base of Q1 to ground), it attenuates the base voltage and renders Q1 with a very small bias current.

Use of Coupling Capacitor

• A capacitor is used to isolate the DC bias network from the microphone , and to short (or “couple”) the microphone to the ampllfifier at hhhigher frequencies.

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DC and AC Analysis • The coupling capacitor is replaced with an open circuit for DC analysis, and then replaced with a short circuit for AC analysis.

Av  gm (RC || rO )

Rin  r || RB

Rout  RC || rO

Bad Output Connection • Since the speaker has an inductor with very low DC resistance, connecting it directly to the amplifier would ~short the collector to ground, causing the BJT to go into deep saturation mode.

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Use of Coupling Capacitor at Output

• The AC coupling indeed allows for correct . However, due to the speaker’s small input impedance, the overall gain drops considerably.

CE Stage with Voltage‐Divider Biasing

Av  gm (RC || rO )

Rin  r || R1 || R2

Rout  RC || rO

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CE Stage with Robust Biasing

VA  

R A  C v 1 RE gm

Rin r ( 1)RE || R1 || R2

Rout  RC

Elimination of Emitter Degeneration for AC Signals

• The capacitor C2 shorts out RE at higher frequencies to eliminate the emitter degeneration.

(VA  )

Av   g m R C

R in  r || R1 || R 2

R out  R C

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Complete CE Stage

 R || R R || R A  C L  1 2 v 1 R || R || R s 1 2 R1 || R2  Rs  RE  gm  1

Summary of CE Concepts

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