EE 382M CMOS Analog Integrated Circuit Design



EE338L CMOS Analog Integrated Circuit Design

Lecture 6, Single-Stage Amplifiers (3)

Cascode Amplifiers

We will cover different cascode amplifiers, including

1. Simple cascode amplifier

2. Multi-level cascode amplifier

3. Gain boosted cascode amplfier

4. Folded cascode amplifier

1. Simple cascode amplifier

[pic]

Large signal behavior (Vin fixed to VG1, Vout (VDS) sweeping from 0 to 3V)

[pic]

Region I: M1B and M2B both in triode; Region II, M1B in saturation, M2B in triode; Region III, M1B and M2B both in saturation

Small signal analysis

We will calculate small signal

i) output resistance,

ii) transconductance (when output is shorted to a fixed DC voltage),

iii) DC voltage gain (when the output is open).

i) Output resistance

We have derived earlier,

[pic]

ii) Transconductance (when output is shorted to a fixed DC voltage or AC ground)

Short the output to an AC ground, and draw the small signal diagram as shown above. According to KCL we can list the following equations,

[pic] (1)

where

[pic] (2a)

[pic] (2b)

[pic]

[pic] (2c)

[pic] (2d)

[pic] (2e)

From Eq. (1), we have

[pic] (3a)

Substitute Eqs. (2c)-(2e) into Eq. (3a), we have,

[pic] (3b)

From Eq. (1), we have

[pic] (4a)

Substitute Eqs. (2a)-(2e) into Eq. (4a),

[pic] (4b)

Solving Eq. (4b), we get

[pic] (5)

Substitute Eq. (5) into Eq. (3b),

[pic] (6)

Thus the transconductance of the cascode amplifier is

[pic] (7)

Observation: Compared with a single-transistor common source amplifier with a transconductance of |Gm|=gm1 (Note that Gm is the transcoducance of the amplifier, and gm is the transcoducance of the transistor), the transcoductance of cascode amplifier is slightly less, whose transconductance Gm is given by

[pic].

iii) DC voltage gain (when the output is open)

[pic]

With the output node open, according to KCL we can list the following equations,

[pic] (8)

where i11, i12, i21, i22, and i23 are expressed by

[pic] (9a)

[pic] (9b)

[pic] (9c)

[pic] (9d)

[pic] (9e)

From Eq. (8), we have

[pic], (10)

Substitute Eqs. (9a) and (9b) into Eq. (10), we have

[pic] (11)

Rearrange the above equation,

[pic] (12)

From Eq. (8), we have

[pic] (13)

Substitute Eqs. (9c) and (9e) into Eq. (13),

[pic] (14)

Rearrange Eq. (14), and substitute vs2 with Eq. (12)

[pic] (15a)

Or

[pic] (15b)

Note that, [pic], Eq. (15b) can be written as

[pic] (15c)

Observation: Assuming the load of the casode amplifier is an ideal current source, the voltage gain of the cascode amplifier is improved compared with single transistor common source amplifier.

[pic]

2. Multi-level cascode amplifier

Large signal behavior

Small signal analysis

i) Output resistance

[pic]

ii) Transconductance

[pic]

iii) Voltage gain

[pic]

Observation: Assuming the load of the amplifier is an ideal current source, the voltage gain of the three-transistor multi-level cascode amplifier is much improved compared with single transistor common source amplifier.

[pic]

3. Gain boosted cascode amplifier

[pic]

Large signal behavior (Vin fixed to VG1, Vout (VDS) sweeping from 0 to 3V)

[pic]

Region I: M1C and M2C both in triode; Region II, M1C in saturation, M2C in triode; Region III, M1C and M2C both in saturation

[pic]

Zoomed-in view of drain currents vs. VDS of simple amplifier, cascode amplifier, and gain boosted cascode amplifier

Small signal analysis

We try to obtain,

i) Output resistance,

ii) Transconductance (when output is shorted to a fixed DC voltage),

iii) DC voltage gain (when the output is open).

of the gain boosted cascode amplifier.

i) Derive the small signal output impedance, rout.

a) Set input voltage to zero (or short vin to ground).

b) Draw the small signal diagram as shown below.

c) Apply itst at the output node.

d) Calculate output voltage vtst.

Note that the current through gds1, i12, equals to itst,

[pic]

Small signal equivalent circuit diagram for calculating output resistance

[pic]. (1)

Note that, vs2 applies to the negative input of the amplifier A. The output voltage of the amplifier A is,

[pic]. (2)

The vgs of M2, vgs2, is given by,

[pic] (3)

Thus, i21 is given by,

[pic]. (4)

The vbs of M2, vbs2, is

[pic], (5)

Thus, i22 is given by,

[pic]. (6)

According to KCL, i21+i22+i23 = itst. We have,

[pic]

(7)

Thus the drain-source voltage of M2, vds2, is given by,

[pic] (8)

Note that, the voltage at the output node, vtst, is given by,

[pic] (9)

Thus, the output impedance (resistance) is given by,

[pic]

(10)

ii) Transconductance (when output is shorted to a fixed DC voltage)

Short the output node of the small signal equivalent circuit to ground, we can draw Fig. 3.

[pic]

Fig. 3. Small signal diagram to calculate transconductance Gm

From Fig. 3, we can list the following equation,

[pic] (11)

Copy Eqs. (4), and (6) below for easy reference,

[pic]. (12)

[pic]. (13)

From Fig. 3, we can list equations for i11, i12, and i23,

[pic], (14)

[pic], (15)

[pic], (16)

Substitute Eqs. (12)-(16) into Eq. (11), we have,

[pic] (17)

Solving Eq. (17), we obtain,

[pic] (18)

Thus

[pic] (19)

Note that, [pic], as [pic], thus Eq. (19) can be re-written as,

[pic], (20)

iii) DC voltage gain (when the output is open).

Small signal voltage gain, Av = Gm rout.

Multiplying Eq. (10) and Eq. (20),

[pic]

(21)

Eq. (21) can also be written as,

[pic] (22)

4. Folded-cascode amplifier

Basic folded-cascode amplifier:

[pic]Fig. 1 Folded-cascode circuit with proper biasing with the source terminal of M1 at VDD (a) and at a suitable bias voltage at VB.

Why choose folded-cascode amplifier instead of telescopic configuration?

• More freedom to choose the DC input voltage at vin (such as Fig. 1(a)).

• Higher voltage swing.

• Convenience in shorting the input and the output in feedback configurations.

Large signal behavior

[pic]

Fig. 2 Large-signal characteristics of folded cascode

In Fig. 2, I1 is the current flowing through M3 and is equal to the sum of ID1 and ID2, VTH1=VT1.

• Vin > VDD-|VT1|, M1 is off and M2 carries all of I1, yielding Vout=VDD-I1RD.

• For Vin ................
................

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