THIẾT KẾ VI MẠCH TƯƠNG TỰƯƠCHƯƠNG 6: Frequency reponse of Amplifiers

TP.Hồ Chí Minh 04/2012

Hoàng Trang-bộ môn Kỹ Thuật Điện Tửhoangtrang@hcmut.edu.vn

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Frequency Response of Amplifiers

1. General Considerations1. General Considerations2. Common-Source Stage3 Source Followers3. Source Followers4. Common-Gate Stage5. Cascode Stage6. Differential Pair6. Differential Pair

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1. General Considerations

Miller Effect Miller Effect Association of Poles with Nodes

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Miller Effect

ill ’ h Miller’s Theorem

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Miller Effect

l Example

Z = 1/CFs/ F

Z1 = [1/CFs]/(1+A)

Z2= [1/CFs]/(1+1/A)Z2 [1/CFs]/(1+1/A)

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Association of Poles with Nodes

We can associate each pole with one node pof the circuit.

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Association of Poles with Nodes

The above statement is not valid in general.g

The location of the poles is difficult to calculate because R3 and C3 create interaction between X and Y.

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2. Common-Source Stage

Schematic

2. Common Source Stage

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2. Common-Source Stage (cont.)

Surmise the transfer function by associating

g ( )

poles with nodes and Miller’s theorem.

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2. Common-Source Stage (cont.)2. Common Source Stage (cont.)

Obtain the exact transfer function.

Sum the currents at each node:

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2. Common-Source Stage (cont.)2. Common Source Stage (cont.)

Ob i h f f i Obtain the exact transfer function.

Writing the denominator

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2. Common-Source Stage (cont.)g ( )

If | 1| | 2| If we assume |ωp1|<<|ωp2|

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2. Common-Source Stage (cont.)g ( )

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2. Common-Source Stage (cont.)

S i h f f i b i i

2. Common Source Stage (cont.)

Surmise the transfer function by associating poles with nodes and Miller’s theorem.

Obtain the exact transfer function.

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3. Source Followers3. Source Followers

S F ll i ll l d Source Followers are occasionally employed as level shifters or buffers.

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3. Source Followers (cont.)( )

T f f i Transfer function

Input impedance Zin Input impedance Zin

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3. Source Followers (cont.)3. Source Followers (cont.)

At relatively low frequencies, gmb >>|CLs|

At high frequencies, gmb <<|CLs|

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3. Source Followers (cont.)3. Source Followers (cont.)

Output impedance

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4. Common-Gate Stageg

S h i Schematic

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4. Common-Gate Stage (cont.)4. Common Gate Stage (cont.)

Transfer function Transfer function

Input impedance

20* See more in Chapter 3

5. Cascode Stageg

C d S b fi i l i Cascode Stage proves beneficial in: Increasing the voltage gain of amplifiers.gain of amplifiers.

Increasing the output impedance of current sources.

Providing shielding as well.

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5. Cascode Stage (cont.)g ( )

U i Mill Eff t d A i ti f Using Miller Effect and Association of Poles with Nodes at node A, X and Y:

Node A:

Node X:

Node Y:

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6. Differential Pair6. Differential Pair

Differential Pair with differential i lsignals.

Differential Pair with active current imirror.

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6. Differential Pair (cont.)6. Differential Pair (cont.)

Differential Pair with differential signals:

The respond is identical to that of a common-

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psource stage.

6. Differential Pair (cont.)( )

Differential Pair with active current mirror:

This circuit has 2 poles:

Mirror pole at node E.

Output pole at output.

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6. Differential Pair (cont.)6. Differential Pair (cont.)

Estimate the frequency response:

CE: the total capacitance at node E, arising

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from CGS3, CGS4, CDB3, CDB1, and the Miller Effect of CGD1, CGD4.

6. Differential Pair (cont.)

Replacing Vin M1 M2 by a Thevenin

6. Differential Pair (cont.)

Replacing Vin, M1, M2 by a Thevenin equivalent, where Vx = gmNrONVin, Rx = 2rON

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6. Differential Pair (cont.)6. Differential Pair (cont.) Assume 1/gmP << rOP. The small-signal voltage

at E is equal to:q

Th ll i l d i t f M4 i V d The small-signal drain current of M4 is gm4VE and – gm4VE –Ix = Vout(CLs + 1/rOP), we have:

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END OF CHAPTER 6

FREQUENCY REPONSE OF AMPLIFIERSAMPLIFIERS

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