summing amplifier revisited

7/28/2019 Summing Amplifier Revisited

1/25

Lecture 5-1

Summing Amplifier Revisited

R4

Superposition can be used to easily evaluate summing amplfiers with infiniteopen loop gain

R1

R2

R3

V1

V2

V3


2/25

Lecture 5-2

Summing Amplifier Revisited

R4

Can we solve for the summing amplifier gain the same way when the openloop gain is finite?

R1

R2

R3

V1

V2

V3


3/25

Lecture 5-3

Other Opamp Nonidealities

The open loop gain is generally so large that we can neglect its impact on theclosed-loop circuit gain

But a significant nonideality that we cannot ignore is the finite open-loopgain as a function of frequency

Parasitic capacitance causes the gain to fall off at high frequency (cant makeH infinite for any amplifier!)

The gain may be designed to change with frequency to enure stability ----compensation


4/25

Lecture 5-4

741 Opamp

One of the most popular, general purpose opamps are the 741-type

+ SINVIN

+ -15VVC1

+ -15VVC2

741OPAMP0

+

-

+

-

VMOUT

3.836 V

+

-

VMIN

0.000 pV

frequency

e-1 e0 e1 e2 e3 e4 e5 e6 e7

-100dB

0dB

100 dB

200dB

DB(VMOUT/VMIN)

frequencye-1 e0 e1 e2 e3 e4 e5 e6 e7

-200

-100

0

PH(VMOUT/VMIN)


5/25

Lecture 5-5

741 Opamp Example

A gain of 10, or 20dB is possible at 10kHz:

time0 2 4 6 8 10 e-4s

-1

0

1V

VMOUT VMIN

+ SINVIN

+

-

VMOUT

1.009 mV

+

-

VMIN

0.000 pV

+ -

-15V

VC8

+ 15VVC9

741OPAMP12

+

-

R15

1E3

R16

10E3


6/25

Lecture 5-6

741 Opamp Example

But not at 100kHz:

+ SINVIN

+

-

VMOUT

1.009 mV

+

-

VMIN

0.000 pV

+ -

-15V

VC8

+ 15VVC9

741OPAMP12

+

-

R15

1E3

R16

10E3

time0.0 0.2 0.4 0.6 0.8 1.0e-4s

-1

0

1V

VMOUT VMIN


7/25

Lecture 5-7

741 Opamp Example

This decrease in gain is evident from a frequency domain analysis


-40

-30

-20

-10

0

10

20

DB(VMOUT/VMIN)


0

100

200

PH(VMOUT/VMIN)

+ SINVIN

+

-

VMOUT

1.009 mV

+

-

VMIN

0.000 pV

+ -

-15V

VC8

+ 15VVC9

741OPAMP12

+

-

R15

1E3

R16

10E3


8/25

Lecture 5-8

Gain as a Function of Frequency

Will the closed-loop gain (with feedback) will always be less than or equal tothe open loop gain as a function of frequency?

frequency

e-1 e0 e1 e2 e3 e4 e5 e6 e7

-100dB

0dB

100 dB

200dB

DB(VMOUT/VMIN)

openloopgain


9/25

Lecture 5-9


We can assume that the close-loop response will follow the open loopcharacteristic beyond the frequency at which they intersect if the loadcapacitance and input terminal capacitances are small

Why are the other capacitors a factor?

frequency

e-1 e0 e1 e2 e3 e4 e5 e6 e7

-100dB

0dB

100 dB

200dB

DB(VMOUT/VMIN)


-200

-100

0

PH(VMOUT/VMIN)

741 Open Loop Characteristics


10/25

Lecture 5-10


It is important that the open loop characteristic has a phase shift of less than180 (a change in gain of less than 40dB per decade) at the point ofintersection with the closed-loop characteristic --- why?

frequency

e-1 e0 e1 e2 e3 e4 e5 e6 e7

-100dB

0dB

100 dB

200dB

DB(VMOUT/VMIN)


-200

-100

0

PH(VMOUT/VMIN)



11/25

Lecture 5-11

Stability

R2

R1

vin

If the open loop gain has a phase shift of 180, and we connect the opampwith negative feedback (which represents another phase shift of 180), thenthe total phase shift will be 360 which is like positive feedback

vo

s

( )A s

( )v

1=


12/25

Lecture 5-12

Feedback

The feedback can further complicate matters if it is also a function offrequency

+

_

Vf

Vo

ViVS

load

( )

input

Af

( ) A ( )1 ( )A ( )+-----------------------------------=

A ( )


13/25

Lecture 5-13

Stability

The circuit will be unstable with this positive feedback

What causes the gain characteristic to exhibit these unwanted phase shifts?

Stable

Marginally Stable

Unstable

open-loop gain

closed-loop gain

f(Hz)

gain(dB)

(phase becomes 180 degreesat some frequency in this range)


14/25

Lecture 5-14

Internal Compensation

Compensation capacitors are added to purposely place a low frequency(dominant) pole so that the change in gain will be 20dB/decade up until theunity gain frequency

Why isnt the phase a concern beyond this frequency?

f(Hz)

gain(dB)

Sacrifices gain for stability

0

20dB/decade


15/25

Lecture 5-15

Feedback

Most feedback weve considered has no phase shift (resistors), socompensation will ensure stability

However, frequency dependent feedback can pose a problem even forcompensated opamps

+

_

Vf

Vo

ViVS

load

( )

input

Af

( ) A ( )1 ( )A ( )+-----------------------------------=

A ( )


16/25

Lecture 5-16

Modeling Gain as a Function of Frequency

With compensation, the frequency response appears like a STC

frequency

e-1 e0 e1 e2 e3 e4 e5 e6 e7

-100dB

0dB

100 dB

200dB

DB(VMOUT/VMIN)


A s( )A

o

1 s b

+----------------------=


17/25

Lecture 5-17

Unity Gain Bandwidth

We can easily solve for the frequency, t, at which the gain is 0dB

frequency

e-1 e0 e1 e2 e3 e4 e5 e6 e7

-100dB

0dB

100 dB

200dB

DB(VMOUT/VMIN)



18/25

Lecture 5-18

Frequency Dependence of Gain

R2

R1

vin

Using these expressions for gain as a function of frequency we canapproximate the inverting amplifier circuit gain as a function of frequency

Vo

Vi

------

R2

R1------

1

1R

2

R1

------+

A s

( )

---------------------+

-------------------------------=

A s( )A

o

1 s b

+----------------------=

Vo

Vi

------

R2

R1------Ao

Ao

1R

2

R1------+

s

b

------- 1R

2

R1------+

+ +

----------------------------------------------------------------------=


19/25

Lecture 5-19


VoV

i

------

R2

R1

------Ao

Ao

1R

2

R1

------+ s

b

------- 1R

2

R1

------+

+ +

----------------------------------------------------------------------=

We can assume that the closed-loop gain is much smaller than the dc openloop gain


20/25

Lecture 5-20


Does this result seem correct?


21/25

Lecture 5-21

Opamp Macromodels

We can model the frequency dependence of the gain using a macromodel forthe opamp

Internal structure of an opamp:

vo

vid1

2+

_

+

_

Gm

C (compensation capacitor)

+1

DifferentialInput Trans-conductance

Amplifier

VoltageAmplifier

Unity-GainBuffer

Well build all of these transistor level components later in the course


22/25

Lecture 5-22

Opamp Macromodels

We can model the first two stages (the last is trivial) using controlled sources,Rs and Cs:

vo

1

2

+

_

C

Gmvid Ro1 Ri2

+

_

vi2

vi2

vo

1

2

+

_

C

Gmvid

R

+

_v

i2

vi2

Which we can simplify by combining the parallel Rs

vid+

_

vid+

_


23/25

Lecture 5-23

Opamp Macromodel

This circuit has the same STC form as a compensated opamp

vo

1

2

+

_

C

Gmvid

R

+

_v

i2

vi2vid

+

_


24/25

Lecture 5-24

Opamp Macromodel

1

2

C(1+)Gmvid

R

+

_

vi2vid

+

_


25/25

Lecture 5-25

Opamp Macromodel

The parameters for a 741 macromodel are:

frequency

e-1 e0 e1 e2 e3 e4 e5 e6 e7

-100dB

0dB

100 dB

200dB

DB(VMOUT/VMIN)


Gm

0.19mA

volt----------= R

o16.7M=R

i24M= 529= C 30pF=

frequency

e-1 e0 e1 e2 e3 e4 e5 e6 e7

DB(VMOUT/VMIN)-100dB

0dB

100 dB

200dB

Macromodel

summing amplifier revisited

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