open loop gain - Carnegie Mellon Universityee321/spring99/LECT/lect5jan27.pdf · • If the open...

Lecture 5-1

Summing Amplifier Revisited

R4

• Superposition can be used to easily evaluate summing amplfiers with infinite open loop gain

R1

R2

R3

V1

V2

V3

Lecture 5-2

Summing Amplifier Revisited

R4

• Can we solve for the summing amplifier gain the same way when the open loop gain is finite?

R1

R2

R3

V1

V2

V3

Lecture 5-3

Other Opamp Nonidealities

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

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

• Parasitic capacitance causes the gain to fall off at high frequency (can’t make ωH infinite for any amplifier!)

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

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

-200º

-100º

0º

PH(VMOUT/VMIN)

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

+ SIN

VIN

+

-

VMOUT

1.009 mV

+

-

VMIN

0.000 pV

+ -

-15VVC8

+ 15VVC9

741OPAMP12

+

-

R151E3Ω

R1610E3Ω

Lecture 5-6

741 Opamp Example• But not at 100kHz:

+ SIN

VIN

+

-

VMOUT

1.009 mV

+

-

VMIN

0.000 pV

+ -

-15VVC8

+ 15VVC9

741OPAMP12

+

-

R151E3Ω

R1610E3Ω

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

-1

0

1V

VMOUT VMIN

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)


0º

100º

200º

PH(VMOUT/VMIN)

+ SIN

VIN

+

-

VMOUT

1.009 mV

+

-

VMIN

0.000 pV

+ -

-15VVC8

+ 15VVC9

741OPAMP12

+

-

R151E3Ω

R1610E3Ω

Lecture 5-8

Gain as a Function of Frequency

• Will the closed-loop gain (with feedback) will always be less than or equal to the 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)

openloop gain

Lecture 5-9


• We can assume that the close-loop response will follow the open loop characteristic beyond the frequency at which they intersect if the load capacitance 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)


-200º

-100º

0º

PH(VMOUT/VMIN)

741 Open Loop Characteristics

Lecture 5-10


• It is important that the open loop characteristic has a phase shift of less than 180º (a change in gain of less than 40dB per decade) at the point of intersection 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)


-200º

-100º

0º

PH(VMOUT/VMIN)


Lecture 5-11

Stability

R2

R1

vin

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

vo s( ) A s( )v1–=

Lecture 5-12

Feedback

• The feedback can further complicate matters if it is also a function of frequency

+

_∑

Vf

VoViVS load

β ω( )

input

Af ω( ) A ω( )1 β ω( )A ω( )+-----------------------------------=

A ω( )

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)

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 the unity gain frequency

• Why isn’t the phase a concern beyond this frequency?

f (Hz)

gain(dB)

• Sacrifices gain for stability

0

20dB/decade

Lecture 5-15

Feedback

• Most feedback we’ve considered has no phase shift (resistors), so compensation will ensure stability

• However, frequency dependent feedback can pose a problem even for compensated opamps

+

_∑

Vf

VoViVS load

β ω( )

input

Af ω( ) A ω( )1 β ω( )A ω( )+-----------------------------------=

A ω( )

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( )Ao

1 s ω⁄ b+----------------------=

Lecture 5-17

Unity Gain Bandwidth

• We can easily solve for the frequency, ωt, 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)


Lecture 5-18

Frequency Dependence of Gain

R2

R1

vin

• Using these expressions for gain as a function of frequency we can approximate the inverting amplifier circuit gain as a function of frequency

VoVi------

R2R1------–

1

1R2R1------+

A s( )---------------------+

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

A s( )Ao

1 s ω⁄ b+----------------------=

VoVi------

R2R1------Ao–

Ao 1R2R1------+

s

ωb------- 1

R2R1------+

+ +

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

Lecture 5-19


VoVi------

R2R1------Ao–

Ao 1R2R1------+

s

ωb------- 1

R2R1------+

+ +

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

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

Lecture 5-20


• Does this result seem correct?

Lecture 5-21

Opamp Macromodels

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

• Internal structure of an opamp:

vo

vid

1

2+

_

+

_

Gm

C (compensation capacitor)

+1µ–

DifferentialInput Trans-conductanceAmplifier

VoltageAmplifier

Unity-GainBuffer

• We’ll build all of these transistor level components later in the course

Lecture 5-22

Opamp Macromodels

• We can model the first two stages (the last is trivial) using controlled sources, R’s and C’s:

vo

1

2

+

_

C

Gmvid Ro1 Ri2

+

_

µvi2–vi2

vo

1

2

+

_

C

Gmvid

R

+

_ µvi2–vi2

• Which we can simplify by combining the parallel R’s

vid+

_

vid+

_

Lecture 5-23

Opamp Macromodel

• This circuit has the same STC form as a compensated opamp

vo

1

2

+

_

C

Gmvid

R

+

_ µvi2–vi2vid

+

_

Lecture 5-24

Opamp Macromodel

1

2

C(1+µ)Gmvid

R

+

_

vi2vid+

_

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 0.19mAvolt----------= Ro1 6.7MΩ=Ri2 4MΩ=µ 529= C 30pF=

frequency

e-1 e0 e1 e2 e3 e4 e5 e6 e7

DB(VMOUT/VMIN)-100dB

0dB

100 dB

200dB

Macromodel

open loop gain - Carnegie Mellon Universityee321/spring99/LECT/lect5jan27.pdf · • If the open...

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