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Chapter 5

Operational Amplifiers and Source Followers

5.1 Operational Amplifier

In single ended operation the output is measured with respect to a fixed potential, usually

ground, whereas in double-ended (Differential) operation the output is measured between,

two nodes those have opposite signal excursions around a fixed point. An important

advantage of differential operation over single ended is higher immunity to environmental

noise. Another common mode rejection advantage at differential operation occurs with

noisy power supply.

5.1.1 The Difference Amplifiers

The convenient way to represent the two input voltages is by their mean and difference

values. The definition of the differential and common mode input voltages by the relations

is given as,

(5.1)

(5.2)

One way of implementing a difference amplifier is to use to single ended amplifier as

shown in Fig. 5.1.

The output would be the difference of two outputs (vo1 and vo2). Similar to the definition of

common mode and differential signals, the common mode and differential output can be

defined as,

(5.3)

(5.4)

The common mode and the differential gains then become as,

(5.5)

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Figure 5.1. Possible implementation of a difference amplifier

(5.6)

A good differential amplifier has high differential gain independent of input common

mode voltage, while the common mode gain should be as low as possible. The common

mode rejection ratio, a figure of merit is defined as,

(5.7)

In simple suggested circuit (Fig. 5.1) the MOSFET currents, and hence the differential gain

will depend on common mode voltage. A good difference amplifier will amplify only

difference signal and not common mode signal. Hence, a better difference amplifier can be

implemented by adding a current source to keep total MOSFET currents constant as shown

in Fig.5.2. When the common mode voltage applied at two inputs changes, the voltage will

get changed only at the node where two sources join (Vs). The current remains unchanged

due to current source and hence the differential gain is unaffected by the common mode

voltage. This gives a high CMRR.

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Figure 5.2. A better implementation of the difference amplifier

5.1.2 Single Ended Differential Amplifier

A single output, which is proportional to the difference between two inputs, is needed very

often. Thus, we need to combine the two outputs. This is achieved using current mirror

loads, as shown in Fig.5.3. We can write,

Figure 5.3. A difference amplifier with single-ended output

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Due to current mirror action, I(Mp2) = I(Mp1). As Mp1 and Mn1 are in series, I(Mp1) =

I(Mn1). Therefore,

(5.8)

Thus, we have single output proportional to difference of inputs. By definition we can

write,

Where, Gm is the equivalent transconductance of differential amplifier stage. The effective

Gm is just the gm of either of the differential pair MOSFETs. Here the output being current,

the circuit is also known as a differential transconductance amplifier. The output voltage of

this circuit is the output current multiplied by the effective output resistance of the stage

[46].

(5.9)

Thus voltage gain can be given analogous to single stage CS amplifier as,

and,

Where, Ctot includes Cdg and Cd of Mn2 and Mp2 respectively and the load capacitance if

any.

5.1.3 Double Ended (Fully) Differential Amplifier

An important application of fully differential amplifiers is their ability to suppress the

effect of common mode interferences [40]. Like CS stage, linear resistors need not be

implemented as the load of a differential pair. The differential amplifier can employ active

load like diode connected or current source as shown in Fig. 5.4.

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Figure 5.4 Differential pair with (a) Diode connected and (b) Current source load

The small signal gain of differential amplifier can be obtained using the half circuit

concept. For Fig.5.4 (a), the load is a MOSFET with gate and drain shorted which becomes

a diode. The impedance offered by diode is (1/gmro) ≈ 1/gm. Where gm is a

transconductance and ro is output resistance of diode connected MOSFET. The differential

gain then becomes

(5.10)

Neglecting ro compared to 1/gm,

(5.11)

However, from (4.16) gm1 is given as

(5.12)

Also realizing the fact that M1 and M3 carry equal currents, voltage gain becomes as

(5.13)

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Similarly the small signal differential gain of current source load differential amplifier can

be found out. The impedances offered by current sources will be ro3 and ro4. Thus the

voltage gain becomes,

(5.14)

The diode-connected load consumes voltage headroom, thus creating a tradeoff between

the output voltage swings, the voltage gain and ICMR. For given bias current and input

device dimensions, the value of gain is decided by overdrive of PMOS diode-connected

device. To get higher gain the aspect ratio of PMOS device must decrease thereby

increasing the overdrive voltage and decreasing the common mode level at the output.

The current source load can provide a relatively higher gain due to the output resistance of

current source device. However, this limits the output voltage swing. To raise the voltage

gain, the output resistance of current source device should be high. This increase in output

resistance maintaining same overdrive voltage is brought by increasing W and L of the

device, which leads to the large capacitance at output node [41].

To alleviate the above difficulty, part of bias currents of input MOSFETs can be provided

by current sources with diode-connected loads as shown in Fig.5.5. The idea here is to

lower the gm of load devices by reducing their current instead of aspect ratio. If M5 and M6

carry eighty percent of drain current of M1 and M2, the current through M3 and M4 is

reduced by five times. For given overdrive of load devices, the transconductance of M3 and

M4 is reduced by five times. Due to this, the differential gain is now five times as that of

only diode-connected load.

Figure 5.5. Differential pair with diode connected and current source load

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5.1.4 Implementation of Single Ended Differential Amplifier

The basic single ended differential amplifiers play a very important role in Monolithic IA.

Hence, we started designing of single ended differential amplifier by replacing source

resistance by improved current sources. The differential amplifier with active load and

single ended output is the commonly used differential amplifier in CMOS analog circuits

(Fig.5.6). This single ended differential amplifier has excellent features in terms of self-

bias capability, common mode rejection, voltage gain and the gain-bandwidth product. In

reference books, the simplified analysis of differential amplifier with active load and single

ended output is specified. The differential voltage gain is evaluated by means of easy

procedure, by replacing MOSFETs with small signal equivalent model. The analysis shows

that the sources at input are at virtual ground for signal in case of pure differential input

[47].

The circuit shown in Fig. 5.6 can be analyzed with some approximations. Using half circuit

concept and replacing MOSFETs with small signal equivalent circuit the differential mode

gain can be found out as,

Figure 5.6. Single ended CMOS differential amplifier with active load and current source

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Similarly, the common mode gain of differential amplifier in Fig. 5.6 can be derived as,

The CMRR is directly proportional to differential mode gain and inversely proportional to

common mode gain. Hence, keeping desired differential mode gain constant, the CMRR

can be increased by using a tail current mirror source with higher output resistance.

Hence, we are replacing tail current source by Wilson current mirror source that has higher

output resistance. The output resistance Ro of Wilson current mirror source from small

signal equivalent model as per (4.73) is given by,

(5.15)

Figure 5.7. Single ended differential amplifier with current source replaced by Wilson mirror

current source.

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This shows that the output resistance of Wilson mirror current source is too larger as

compared to the tail current mirror source in Fig. 5.6. Thus, improvement in CMRR can be

expected.

The complete circuit of single ended differential amplifier with modified current source is

shown in Fig. 5.7. The simulated results are shown in Table 5.1 with the size of MOSFETs

selected as M1,2 = 40/1 µm/µm, M3,4 = 58/0.25 µm/µm, M5,6,7,8 = 10/0.25 µm/µm. The

CMRR is seen to be increased by 10 times.

Table 5.1: Simulated Results

Parameters Differential amplifier with

current mirror source

Differential amplifier with Wilson

mirror current source.

Vd 1mV 5mV

Vod 113mV 555mV

Ad 113 111

Vc 1V 1V

Voc 40mV 3.02mV

Ac 0.04 0.003

CMRR 69 dB 91.36 dB

5.1.5. Implementation of Double Ended (Fully) Differential Amplifier

The load of a double differential amplifier can be diode connected or current source. The

diode-connected load consumes voltage headroom thus reducing the output voltage swing,

voltage gain and input CM range [50]. The current source load can provide higher voltage

gain but at the cost of higher drain to source voltage required to keep MOSFET in

saturation. In order to overcome the difficulty with diode connected and current source

loads the part of bias current of input MOSFETs M1, M2 can be provided by PMOS current

sources as shown in Fig. 5.8.

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Figure 5.8. Double ended Differential Amplifier with diode connected and current source

Loads

The idea is to lower the gm of load devices by reducing their current instead of their aspect

ratio (W/L)P. If M5 and M6 carry 80% of drain current of M1 and M2, the current through

M3 and M4 gets reduced by five times. This translates to a factor of five reduction in

transconductance of M3 and M4, hence as per (1) the differential gain increases by five

times. The small signal gain of above balance differential amplifier will be in the range of

10 to 20 and the common mode gain will get reduced by five times as compared to diode

connected loads [11][18]. The simulated results are as shown in Table 5.2.

Table 5.2: Simulated Results of Double Ended Differential Amplifier

Parameters

Simulated results for

Diode Load Current source

Load Combined Load

Ad 3.05 7.15 23

Ac 0.055 0.067 0.06

CMRR 34.87 dB 40.56 dB 51.67 dB

5.2 Operational Amplifiers (Op Amp)

An operational amplifier is roughly defined as a high gain difference amplifier. High

means a value adequate for the applications, typically in the range of 101 to 10

5. Op amps

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are usually employed in a feedback system; hence, their loop gain is selected according to

the precision required for the closed loop system blocks. The efforts to serve as general-

purpose building block sought to create an ideal op amp, with very high voltage gain, high

input impedance, and low output impedance but at the cost of speed, output voltage

swings, and power dissipation [48]. Nowadays op amp design proceeds with realizing the

trade-off between the parameters. Let us consider following op amp design parameters

with importance and significance of each [42].

Gain

The open loop gain of op amp determines the precision of the feedback system utilizing the

op amp. Depending on application, the required gain may vary by four orders of

magnitude. To compromise with speed and output voltage swings, the minimum required

gain must be known. A high open loop gain may also be necessary to reduce nonlinearity.

Small-Signal Bandwidth

The high frequency behavior of op amp is desired in many applications. The open loop

gain begins to drop with increase in frequency of operation, thus creating larger errors in

the feedback system. The small signal bandwidth is usually defined as the unity-gain

frequency fu, which is greater than 1 GHz for today‘s op amps. Sometimes the 3-dB

frequency, f3-dB, may also be specified.

Large-Signal Bandwidth

Op amps must operate with large transient signals in many modern applications. The

nonlinear phenomena of op amp make it difficult to characterize the speed by simply small

signal properties such as the open loop response. The large signal analysis shows that a

large difference momentarily drives op amp into a nonlinear region of operation.

Output Swing

Many applications of op amp require large voltage swings to accommodate a wide range of

signal amplitudes. Fully differential op amps became quite popular with need for large

voltage swings. The double-ended differential amplifier circuits generate complementary

outputs, thereby doubling the available swing. As seen from analog design octagon and

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chapter earlier, the maximum voltage swing trades with device size and bias currents and

hence speed. Achievement of large swings is also one of the challenges in today‘s op amp

design.

Linearity

Op amps if operated in open loop suffer from substantial nonlinearities. In large gain

differential amplifiers, the input pair of MOSFETs exhibits a nonlinear relationship

between its differential drain current and input voltage. This problem of nonlinearity is

tackled by two approaches one using fully differential form to suppress even-harmonics

and secondly setting high open loop gain such that closed loop feedback system achieves

adequate linearity. Actually, in many feedback systems linearity rather than the gain error

requirement decides the choice of the open-loop gain.

Noise and Offset

The minimum signal level processed faithfully is determined by the input noise and offset

of op amp. In op amp circuits, several devices decide noise and offset thus requiring large

dimensions or bias currents. The trade off also exists between noise and output swing.

With a given bias current, the overdrive of the load devices is lowered to permit larger

swings at the output, thus transconductance increases and also drain noise current.

Supply Rejection

Many times op amps are used in mixed-signal systems and connected to noisy digital

supply lines. The performance of op amps in presence of noise is quite important

especially with increase in noise frequency. Fully differential topologies are used for this

purpose.

5.2.1 One Stage Op-Amps

All the differential amplifiers studied in earlier sections can be considered as op amps.

Two topologies of differential amplifiers are shown in Fig. 5.9, single-ended and double-

ended (differential) outputs. The small-signal low-frequency gain of both the circuits is

given by gmN (roNroP), where the P and N subscripts denote NMOS and PMOS devices.

This value of gain provided by single stage differential amplifiers scarcely exceeds 20 in

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submicron devices with typical currents. Generally, the bandwidth is determined by inter

electrode capacitances and load capacitance, CL. The single-ended differential amplifier

circuit exhibits a mirror pole whereas the double-ended does not. This difference is critical

as far as stability of circuit is concerned. Both the circuits suffer from noise contributed by

MOSFET devices. To achieve high gain the differential cascode topologies can be used as

shown in Fig.5.10. These cascode configurations of both single-ended and differential

Figure 5.9. Simple op-amp topologies

output op amps provide a gain of the order of gmN[(gmNr2

oN) (gmPr2

oP), but at the cost of

reduced output swing and added pole. These configurations are known as telescopic

cascode op amps. The single-ended cascode op amp circuit offers a mirror pole at node X,

thus creating stability issue.

The output swing of differential output cascode op amp is given by 2[VDD-

(VOD1+VOD3+VCSS+|VOD5|+|VOD7|)]. This shows that the output swings of telescopic

cascode op amps are limited compared to simple op amps.

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Figure 5.10. Cascode op amps

The difficulty in shorting inputs and outputs is another drawback of the telescopic cascode

op amp. This is required when op amp is used as a buffer but then cascode op amp will

work for certain range of input as a buffer.

Above two drawbacks of telescopic cascode op amps are overcome by folded cascode op

amp. The folded cascode op amp also will offer the capability of handling input common-

mode levels close to supply voltage.

Telescopic cascode op amps can also be designed to provide a single-ended output. The

cascode current mirror load converts the differential currents of main devices M3 and M4 to

the single-ended output voltage as depicted in Fig.5.11 (a). However, here the voltage at X

is given as VX=VDD-|VGS5|-|VGS7| and the output voltage VOUT is limited to VDD-|VGS5|-

|VGS7|+|VTH6|. Thus one PMOS threshold voltage is wasted in the output swing. To

improve the output voltage swing the PMOS load can be modified as shown in Fig. 5.11

(b). Here the MOSFETs M7 and M8 are biased at the edge of the triode region. Actually the

circuit of Fig. 5.11(a) suffers from two disadvantages as compared to its counterpart in Fig.

5.11(b). First, it provides only half the maximum output voltage swing. Secondly, it

includes a mirror pole at node X, thus limiting the speed of feedback systems using such

amplifier.

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Figure 5.11.Cascode op amps with single-ended output

5.2.2 Design Example

Statement: Design a fully differential telescopic op amp with specifications as : VDD =

3V, differential output maximum swing = 3V, power dissipation less than 0.5 mW,

Voltage gain 1500. Assume µnCox = 60µA/V2, µpCox = 30µA/V

2, λn = 0.11V

-1, λp = 0.22V

-1

(for effective channel 0.5µm), body effect coefficient γ = 0, VTHN = |VTHP| = 0.7V.

Design Steps -

The op amp topology along with two current mirrors fixing the drain currents of M7 - M9 is

shown in Fig 5.12. Let us begin with power dissipation, total current available is 0.167mA

out of which half will be required for current mirrors and half available for the circuit.

Each cascode branch thus carries a current around 40µA. The required output swing is 3V

differential, thus each output node must be able to swing by 1.5V without driving any of

the MOSFET into triode region. Therefore the total voltage available for M9 and each

cascode branch is equal to 1.5V. Hence, |VOD7|+ |VOD5| + VOD3 + VOD1 + VOD9 = 1.5V. As

M9 carries maximum current 80µA, choosing VOD9 = 0.5V, leaving 1V for remaining four

MOSFETs in cascode branch. Also M5- M8, being PMOS suffer from low mobility, thus

allocating over drive of 300mV approximately to each. Finally remaining 400mV is

allocated between M1 and M3, 200mV each.

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Figure 5.12. Op amp topology along with two current mirrors

With drain current and overdrive voltage known of each MOSFET, the aspect ratio can be

found out from (4.6) of drain current. To get lower device capacitances the minimum

channel length of MOSFET is selected 0.5µm. Thus we get the aspect ratios as

(W/L)1-4 = 11, (W/L)5-8 = 14, (W/L)9 = 4.

Now to find out theoretical voltage gain, gm and ro will be required of MOSFETs which

can be calculated using (4.15) and (4.17)

gm1-4 = 4 x 10-4

A/V, gm5-8 = 2.67 x 10-4

A/V

ro1-4 = 227.2kΩ, ro5-8 = 113.63kΩ

The voltage gain of telescopic cascode op amp

A ≃ gm1 [(gm3 ro1ro3)( gm5 ro5ro7) = 1179

This gain is much lower than the desired gain 1500. To increase the gain we recognized

that gmro ∝ √(WL/ID). Thus keeping ID constant the gain can be increased by scaling W and

L simultaneously keeping ratio constant.

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Figure 5.13 Schematic of Telescopic cascode op-amp

As M1 – M4 appear in signal path, to keep their capacitances minimum their size will not

be scaled. The PMOS devices M5 – M8 affect the signal to smaller extent and hence are

scaled. By scaling W and L, ro gets scaled while gm remains constant. Let us assume that

scaling is done 1.4 times, therefore (W/L)5-8 will be 21/0.7. Also λp gets reduced by 1.4

times that is 0.16. Modified PMOS devices, now will require slightly larger overdrive due

to increase in dimension. Thus allotting 50mV more to M5-8 and reducing overdrive of M9

by 100 mV. The new dimension of M9 comes out to be (W/L)9 = 16. Now calculated gain

comes out to be around 1650. The schematic of telescopic cascode op-amp simulated is

shown in Fig. 5.13 and frequency and phase response comes out to be as shown in Fig.

5.14.

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Figure 5.14 Frequency and phase response of Telescopic cascode op-amp

5.3 Source Followers

A high voltage gain can be achieved from common source amplifier with high load

impedance. If amplifier is required to drive a low impedance load then a buffer must be

placed after amplifier. A buffer will drive the low impedance load with negligible loss of

signal strength [53]. The common drain stages (source followers) are used as building

blocks in a large number of high speed or high frequency applications, due to their intrinsic

simplicity and wideband characteristics. The source followers suffer from non-ideal effects

such as body effects, channel length modulations, signal-dependent capacitive effects and

frequency distortions arising from capacitive loads. These non-ideal effects create a trade

off among linearity, bandwidth and power dissipation. The analysis of source followers is

based on non-linear parameters gm, gmb and ro in a low frequency small signal model.

For NMOS source follower (NSF) as well as PMOS source follower (PSF), the input

signal is applied to the gate and output is taken from the source. For signal levels above

threshold voltage, the output voltage is equal to input voltage minus gate source voltage

[52]. The gate source voltage consists of threshold and over drive voltage. If both these

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voltages are constant, then output voltage is simply input voltage added with offset. The

small signal gain would then be unity. Thus, the source follows the gate and circuit is

known as a source follower. Actually threshold voltage depends on the body effect and the

over drive depends on drain current. Also even if the drain current is kept constant, the

overdrive depends to some extent on the drain-source voltage. Small signal equivalent

circuits of MOSFETs with body effect can be used to evaluate the analysis of source

follower circuits.

5.3.1 NMOS and PMOS Source Follower

A. Small Signal Analysis of NSF

The NSF in Fig. 5.15 consists of NMOS input transistor and NMOS current source as a

load. The input signal Vi consists of the DC biasing voltage VTH and the ac signal vi

whereas the output signal Vo consists of a DC biasing voltage VDS and the ac signal vo. For

n-well process, the bulks of M1and M2 share the same substrate. Hence, NSF suffers from

the body effect.

Figure 5.15 NMOS Source follower (NSF) circuit

The small signal equivalent circuit of NSF is shown in Fig. 5.16. The body terminal is

connected to lowest supply voltage (ground) to maintain source-body pn junction reverse

biased. Since source is connected to output, vbs changes with output and gmb generator is

active [1]. The load current source formed with M2 is replaced by its drain resistance ro2.

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Figure 5.16 Small signal equivalent circuit of NSF

Applying KVL around input loop,

(5.16)

When the output is open circuited, io= 0 and applying KCL at output node gives

(5.17)

From (5.16) substituting for vgs into (5.17) and rearranging,

(5.18)

If load current source is ideal, , (5.18) simplifies to

(5.19)

If ro1 is finite, the open circuit voltage gain of source follower is less than unity even if

body effect is neglected. The variation in output voltage changes the drain-source voltage

and the current through ro1. The large signal analysis shows that the over drive on gate also

depends on the drain source voltage unless channel length modulation is negligible. This

causes the small signal gain to be less than unity.

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If ,

(5.20)

Equation (5.20) shows that the voltage gain of the source follower is less than unity and it

depends on = , which is typically in the range of 0.1 to 0.3. In addition, χ depends on

source-body voltage, which is equal to vo when the body is grounded. Hence, gain found

out in (5.20) depends on output voltage, causing distortion for large signal changes in the

output. This can be overcome by selecting the type of source follower n-channel or p-

channel fabricated in an isolated well. The well can be connected to source making vsb =0.

In this case the parasitic capacitance from well to substrate increases reducing the

bandwidth of source follower.

The output resistance of source follower can be calculated from Fig. 5.16 by driving the

output with a voltage source vo and setting vi = 0.

(5.21)

Then,

(5.22)

It is seen that the body effect reduces the output resistance, which is desirable as the source

follower produces a voltage output. This desired effect results from the nonzero small

signal current drawn by the gm generator. As →∞ and →∞, this output resistance

becomes , same as input resistance of common gate amplifier. The source

followers are used as buffers and level shifters. They are more flexible as a level shifter

because the dc value of VGS can be adjusted by changing aspect ratio W/L.

B. Small Signal Analysis of PSF

With the circuit of PSF, the most of designs have utilized a body tied PMOS input

transistor to remove the bulk modulation effect and to improve the precision. This is

possible as PMOS and NMOS transistors share the same substrate. Due to lower mobility

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of PMOS devices, this results in higher output impedance than NSF. Also the

transconductance efficiency is low in PSFs which results into small drive ability and a

larger silicon area.

Fig. 5.17 shows a conventional PSF in an n-well process which includes a PMOS input

transistor and a PMOS current source. The small signal equivalent model for PSF will be

same as NSF. In high frequency equivalent model, PSF will have additional capacitance

due to bulk-well. In addition, the channel length modulation coefficients of M1 and M2 in

PSF are smaller than that of NSF. This gives better linearity of PSF.

Figure 5.17. PMOS Source follower (PSF) circuit

5.3.2 The Super Source Follower

The output resistance of source follower is approximately 1/(gm+gmb). As MOSFETs have

much lower transconductance, this output resistance may be too high especially when a

resistive load is to be driven. The output resistance can be reduced by increasing

transconductance with increase in aspect ratio W/L of source follower and its dc bias

current. This requires a proportionate increase in the area and power dissipation. To

minimize the area and power dissipation required for low Ro, the source follower

configuration is used as shown in Fig. 5.18.The super follower as shown in Fig. 5.18 uses

negative feedback through M2 to reduce the output resistance [36].The qualitative analysis

shows that, when the input voltage is constant and the output voltage increases; the drain

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current of M1 also increases, resulting into increased gate-source voltage of M2.As a result,

the drain current of M2 increases, reducing the output resistance.

Figure 5.18 Super-source follower circuit

The dc bias current in M2 is the different between I1 and I2, thereforeI1> I2 is required for

proper operation. This condition can be used to find small signal parameters of MOSFETs.

The small signal equivalent circuit is shown in Fig. 5.19. The body effect of M2 is

neglected becausevbs2= 0. The polarities voltage controlled current sources for NMOS and

PMOS are identical. The current sources I1 and I2 are replaced by their internal resistances

r1 and r2 respectively. If the current sources I1 and I2 are ideal, ro1→∞ and ro2→∞. For

practical current sources these resistances are large but finite.

To find output resistance of the super source follower, set vi =0 and find the current io that

flows into the output node when it is driven by a voltage vo. Applying KCL at output

under these conditions to Fig. 5.19,

(5.23)

Similarly applying KCL at drain of M1 with vi = 0,

(5.24)

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Substituting for v2 from (5.24) into (5.23) and rearranging gives,

(5.25)

Consider I1 and I2 ideal, r1→∞ and r2→∞. Also if ro2→∞ and (gm1+gmb1) ro1>>1,

(5.26)

Figure 5.19 Small signal equivalent circuit of super source follower

This is the output resistance of super source follower. Comparing (5.26) with (5.22), shows

that the negative feedback through M2 reduces the output resistance by a factor of about

gm2ro1 .

The open circuit voltage gain of super source follower can be found out from small signal

equivalent circuit with the output open circuited. Applying KCL at the output node gives,

(5.26)

Also applying KCL at drain of M1 gives,

(5.27)

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Substituting for v2 from (5.26) into (5.27) and rearranging gives,

(5.28)

Assuming ideal current sources gives,

(5.29)

Comparing the open circuit voltage gain of the super source follower (5.29) with the open

circuit voltage gain of a simple source follower (5.19) it is seen that the deviation of this

gain from unity is greater in super source follower than a simple source follower. If,

, this difference is small and the conclusion is that the super source follower

has little effect on the open circuit voltage gain.

The product gmro for MOSFET is given by relation

Where µ is mobility of charge carriers, Cox is gate oxide capacitance, λ is channel length

modulation coefficient and W/L is aspect ratio.

In addition, λ α 1/L, hence we get

Therefore, the width and length can be adjusted to get desired product gmro without

changing Id.

5.3.3 Design Example

Statement: Design a source follower with VDD= 3V, ID= 1 mA, having voltage gain close

to unity output resistance not more than 100Ω and to handle input 2Vp-p.

Design steps -

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As voltage gain desired is close to unity, the PMOS source follower with current source

load as shown in Fig.5.17, will be preferred which has got less severe body effect

compared to NMOS.

Now from data given,

And

(Say which is close to unity)

Thus we get,

gm1=0.0099

To find overdrive,

Therefore,

The overdrive for M1 can be calculated using relation,

Thus Vod1=0.202 V

Now the drain currents of both MOSFETs will be equal and given as,

And

As both MOSFETs carry same current above equations can be equated giving,

We get,

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Thus,

Assuming wide band application let L= 0.5 µm, maximum value of Vod2 is 0.798 V, but

allotting Vod2= 0.65 V. Then we get,

Figure 5.20 Schematic of PSF

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Figure 5.21 Frequency and phase response of PSF

If (W/L)1=1000 , (W)1= 500 µm.

(W/L)2= 113.6 let take 120, (W)2=60 µm.

The schematic of PSF simulated is shown in Fig. 5.20 and as expected, the wide band

frequency response is obtained as shown in Fig. 5.21.

This chapter deals with the different configurations of the differential amplifiers used in

the schematic of IA. The detailed designing of the telescopic cascode op amp is carried out

which forms basis for the designing of various circuits in the IA. The last stage in most of

the monolithic circuits is a buffer. The buffer can be designed using NMOS or PMOS

source followers but one designed with PMOS gives properties close to a good buffer. The

function of level shifter also is well accomplished by source follower.

*****