Tim Green, Linear Applications 520-750-2193 [email protected] 1 Measuring Zo in SPICE Preferred Test Circuits and Why? Brought to you by: The Wizard of.

Tim Green, Linear Applications

520-750-2193 [email protected]

1

Measuring Zo in SPICE

Preferred Test Circuits and

Why?

Brought to you by: The Wizard of Zo



2

Measuring Zo in SPICE Aol Test

+Vs 2.5

-Vs 2.5

Vo

VL 0

RL 100

LT 1.0E+15

C1 1.0E+15

+ VG1

-

++

4

3

5

1

2

U1 OPA376

Aol = Vo

-25.384449uV

Aol Test.TSC



3

Measuring Zo in SPICE Aol Test T

Aol @ DC

Frequency (Hz)

10m 100m 1 10 100 1k 10k 100k 1M 10M

Ga

in (

dB

)

-20

0

20

40

60

80

100

120

140

160

Aol @ DC

Aol @ DC = 144.13dB

Linear Aol @ DC = 10

dB

20

Linear Aol @ DC = 10

144.13

20

Linear Aol @ DC = 16.0879Meg

Vo A:(32.050326m; 144.134867)

Aol Magnitude

a



4

Measuring Zo in SPICEClosed Loop Gain

+Vs 2.5

-Vs 2.5

Vo

RL 100

-

++

4

3

5

1

2

U1 OPA376

RF 16.0879G

LT 256T

+

VG1

-25.384449uV

Set RL = 100 ohms;

Low enough for no Ibias issues and low enough for no Cin issues

Set Closed Loop Gain = 10x (Aol @ DC);

ensure op amp w ill run in open loop for frequencies of interest

RF = RL 10 (Aol @ DC)

RF = 100 10 16.0879M = 16.0879G

Select LT for the low est frequency of interest (fz)

fz = RF

LT2

For our example choose fz = 10Hz

fz = RF

LT2 implies LT = RF

fz2

LT = 16.0879G

10Hz2 = 2.56e14 = 256THClosed Loop Gain.TSC



5

Measuring Zo in SPICEClosed Loop Gain T

Frequency (Hz)

10.00p 1.00n 100.00n 10.00u 1.00m 100.00m 10.00 1.00k 100.00k 10.00M

Ga

in (

dB

)

-20

0

20

40

60

80

100

120

140

160

Vo A:(1.020092m; 143.343148)

Closed Loop Gain

a



6

Measuring Zo in SPICE1/Beta Test

+Vs 2.5

-Vs 2.5

Vo

RL 100

-

++

4

3

5

1

2

U1 OPA376

R1 15.8G

LT 251.46T

L1 1.0E+15

C1 1.0E+15

+ VG1

VFB

1/Beta = 1/VFB

-25.384449uV

-25.384449uV

One_Beta Test.TSC



7

Measuring Zo in SPICE1/Beta Test T

Frequency (Hz)

10p 1n 100n 10u 1m 100m 10 1k 100k 10M

Ga

in (

dB

)

40

60

80

100

120

140

160

180

Closed Loop Gain (1/Beta) > 10uHz = 163.973dBAol @ DC = 144.13dB

Closed Loop Gain = 10x (Aol @ DC)Closed Loop Gain = (20dB + Aol @ DC)

1/Beta 1/Beta A:(255.603954; 163.973142)

a



8

Measuring Zo in SPICEAol, 1/Beta, Closed Loop Gain

T

Aol

1/Beta

Closed Loop Gain

Frequency (Hz)

10p 1n 100n 10u 1m 100m 10 1k 100k 10M

Ga

in (

dB

)

-20

0

20

40

60

80

100

120

140

160

180Aol, 1/Beta, Closed Loop Gain

Closed Loop GainAol

1/Beta



9

Measuring Zo in SPICEFinal Zo Test Circuit - Unloaded

+Vs 2.5

-Vs 2.5

Vo

ITVL 0

A+

IdcRL 100

RF 16.0879G

LT 256T

-

++

4

3

5

1

2

U1 OPA376

DC = 0A

AC = 1Apk

-253.845264nA

-25.384449uV

Op Amp Zo Test

Zo = Vo

Scale Logarithmic to remove 20 Log (Vo / IT)

Log scale -> Zo = Vo in ohms

Loaded Zo Test:

Idc = VL / RL

Test Loaded Zo for both +Idc and - Idc

Unloaded Zo Test:

Set VL = 0VOp Amp Zo SPICE Measure.TSC



10

T

Vo / IT = Zo (dB)

Frequency (Hz)

10p 1n 100n 10u 1m 100m 10 1k 100k 10M

Ga

in (

dB

)

-40

-20

0

20

40

60

80

Zo Test CircuitUnloaded ZoVo / IT = Zo (dB)

Vo / IT = Zo (dB)

Measuring Zo in SPICEFinal Zo (dB) Test Circuit - Unloaded

Below fx Zo is not valid

fx



11

Measuring Zo in SPICEFinal Zo (ohms) Test Circuit - Unloaded

T

Vo / IT = Zo (ohms)

Frequency (Hz)

10p 1n 100n 10u 1m 100m 10 1k 100k 10M

Zo

(o

hm

s)

20m

200m

2

20

200

2k

20k

200kZo Test CircuitUnloaded ZoVo / IT = Zo (ohms)when Vo / IT scale is changed to Logarithmic as it removes the 20Log (Vo\IT) scaling.

Vo / IT = Zo (ohms)

fx




12

Measuring Zo in SPICEFinal Zo Test Circuit – Loaded Source

+Vs 2.5

-Vs 2.5

Vo

ITVL 200m

A+

IdcRL 100

RF 16.0879G

LT 256T

-

++

4

3

5

1

2

U1 OPA376

DC = 0A

AC = 1Apk

1.999713mA

199.97133mV



13

Measuring Zo in SPICEFinal Zo Test Circuit – Loaded Source

T

Frequency (Hz)

10p 1n 100n 10u 1m 100m 10 1k 100k 10M

Zo

(o

hm

s)

10m

100m

1

10

100

1k

10k

Zo Test Circuit Loaded Zo - 2mA Source

Vo A:(26.499429u; 1.493863k)

a


fx



14

Measuring Zo in SPICEFinal Zo Test Circuit – Loaded Sink

+Vs 2.5

-Vs 2.5

Vo

ITVL -200m

A+

IdcRL 100

RF 16.0879G

LT 256T

-

++

4

3

5

1

2

U1 OPA376

DC = 0A

AC = 1Apk

-2.000222mA

-200.022173mV



15

Measuring Zo in SPICEFinal Zo Test Circuit – Loaded Sink

T

Frequency (Hz)

10p 1n 100n 10u 1m 100m 10 1k 100k 10M

Zo

(o

hm

s)

10m

100m

1

10

100

1k

10k

Vo A:(35.254154u; 1.077298k)

Zo Test Circuit Loaded Zo - 2mA Sink

a

fx




16

Measuring Zo in SPICEFinal Zo Test Circuit – Complete Zo Curves

T

Zo 2mA Sink

Zo 2mA Source

Zo Unloaded

Frequency (Hz)

10p 1n 100n 10u 1m 100m 10 1k 100k 10M

Zo

(o

hm

s)

2m

20m

200m

2

20

200

2k

20k

Zo Unloaded

Zo 2mA Source

Zo 2mA Sink


fx



17

Appendix – Ro Derivation Op Amp Model for Derivation of ROUT

+

-

RDIFF

xAol

RO-IN

+IN

-

+

VE

Op Amp Model

1A

VOUT

VO

RF

RI

IOUTVFB

ROUT = VOUT/IOUT



18

Appendix – Ro Derivation

= VFB/VOUT = [VOUT (RI / RF + RI)]/VOUT = RI / (RF + RI)

ROUT = VOUT/IOUT

VO = -VE Aol

VE = VOUT [RI/(RF + RI)]

VOUT = VO + IOUTRO

VOUT = -VEAol + IOUTRO

VOUT = -VOUT [RI/(RF + RI)] Aol+ IOUTRO

VOUT + VOUT [RI/(RF + RI)] Aol = IOUTRO

VOUT = IOUTRO / 1+[RIAol/(RF+RI)]

ROUT = VOUT/IOUT =[IOUTRO / 1+[RIAOL/(RF+RI)]]/IOUT

ROUT = RO / (1+Aol)

Derivation of ROUT (Closed Loop Output Resistance)



19

Appendix – Ro Derivation OPA353 Specifications

RO = 40Ω

ROUT (@1MHz, G=10) = 10Ω

Aol @1MHz = 29.54dB = x30



20

Appendix – Ro Derivation OPA353 ROUT Calculation

+

-

RDIFF

xAol

RO-IN

+IN

-

+

VE

Op Amp Model

0.1mA

VOUT

VO

RF

RI

IOUTVFB

ROUT = VOUT/IOUT

1mV

9k

1k

x29.54dBx30

ROUT = 1mV/0.1mAROUT = 10

0.1mV

3mV

+- 4mV

+

-

RO = 40Ω

ROUT (@1MHz, G=10) = 10Ω

Aol @10mHz = 29.54dB = x30

VOUT = IOUTRO / 1+[RIAol/(RF+RI)]



21

Appendix – Ro Derivation ROUT vs RO

• RO does not change when feedback is used to close the loop

• Closed loop feedback forces VO to increase/decrease

• The increase/decrease in VO appears at VOUT as a

reduction in RO

• ROUT is the net effect of RO and closed loop feedback controlling VO

Tim Green, Linear Applications 520-750-2193 [email protected] 1 Measuring Zo in SPICE Preferred Test Circuits and Why? Brought to you by: The Wizard of.

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