F.Tang 50

Modeling for MCP-PMT Output Signal1. Modeling with RC Load

• Mathematic modeling

• Spice simulation with linear-rise Impulse force

• Spice simulation with 2-τ exponential force

• Comparison between simulation and test

2. Modeling with RLC Load (and includes T-line)

• Mathematic modeling

• Spice simulation

• Comparison between simulation and test

3. Summary

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Camden’s Test

60mV420.4ps1.2p1

80mV477.4ps1.5p4

117mV478.0ps2.3p9

145mV480.0ps2.8p16

Vp(test)Tr(test)Capixel

16-pixel 9-pixel

4-pixel

1-pixel

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Tube and AnodesAnode Pads

elastomer

From Jean-Francois’ calculation:

The tube current source should be linearly rise

in a time interval of 75ps-225ps, which is

related to tube structure and the field

between MCP_out to anode, then suddenly

stops, we call it as “linear-rise impulse”

“linear-rise impulse”

75ps-225ps for different tubes

t

i

SMAs

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CIf the current source is a impulse, then

rise time of output pulse is a step

function, amplitude is proportional to

1/C, then decay with τ=RC.

Modeling for Tube’s Output with RC Load

Rise Time is Nothing Dependent If

Input is a Impulse Current Source!

Ignore slow current path

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Effect of C_anode to the Rise Time of Output Signal (1)

Input force: Linear-rise Impulse Current Source (tr=100ps, tf=1ps, Ip=1A)

Outputs by Sweeping C from 1pF to 10pF

with R=infinite

Input Force

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Effect of C_anode to the Rise Time of Output Signal (2)

Input force: Linear-rise Impulse Current Source (tr=100ps, tf=1ps, Ip=1A)

Output by Sweeping C from

0.1pF to 3.6pF with 0.5pF step

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Tube’s Rise Time Dependency with Finite Rise Time Exp-type Input

Sweep C from

0.5p -4p

Effect of C_anode to Rise Time of Output Signal (1)

Input force: 2-τ Exponential Current Source (tr=100ps, tf=300ps)

Input force

Outputs by Sweeping C

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Sweep R from

50-500 ohms

Effect of C_anode to Rise Time of Output Signal (2)

Input force: 2-τ Exponential Current Source (tr=100ps, tf=300ps)

Input force

Outputs by Sweeping R

Tube current should

not work like that!

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Modeling for Tube’s Output With LRC Load

= 1)( 2 ++

+=

sRCLCsRsLsVa

RsLR

sRCLCsRsLsVo

+•

+++

=1

)( 2

LLedge

C

Ignore slow current path

i=δ(t)

MCPOUT is an AC ground for fast signal

Vo

R

Transfer Function:

Laplace transform with impulse current force:

Fast signal components: 2-Pole!

Va

12 ++=

sRCLCsR

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MCP-PMT Model with Anode L and C

Swept C from 1pF to 10pF , We

see the rise time of output pulse

is a function of C_anode

C_scope

Pulse shape is very close to our test pulse shape

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Comparison of Output Pulse Shapes

Simulation Test

16-pixel16-pixel

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Model with LRC and T-line

Scope InputMCP-PMT

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Summary

• Model with RLC seemed accurate.

• Output pulse shape from simulation is very consistent to the one we obtained from scope.

• Similar output behaviors have been observed from simulation as Photek obtained from their tests.

• More tunes on both model and shape of current source may be needed for further comprehensive simulations