Goto:   Coaxial
Section      Output
Format        Notes

Definition:

Equation

Parameters

Diagram

Calculate Properties of a Vdot
Probe:
top

Parameter

Value

Units

Special
Values

Inputs:

A
(probe area)

square
meterssquare centimeterssquare
millimeterssquare micrometerssquare nanometerssquare
inchessquare feetsquare milssquare
yardssquare milessquare
kilometerssquare lightyears____________________

d
(probe distance)

inchesmeterscentimetersmillimetersmicrometersnanometersfeetmilsyardsmileskilometerslightyears____________________

Alternate
version uses V1 and E on probe surface

er (dielectrc
const.)

1 for
vacuum

R
(load resistance)

OhmskiloOhmsMegaOhmsmilliOhmsmicroOhmsnanoOhms____________________

usually 50
Ohms

C2 (stray
capacitance)

pF,
picofaradsF, FaradsmF,
millifaradsuF, microfaradsnF,
nanofarads____________________

enter 0 to
ignore

dV1 (voltage
rise)

VoltskilovoltsMegavolts____________________

only
needed to calculate V2

dt (rise time)

secondsnanosecondsmicrosecondsmillisecondsdayhour (h)minute
(min)sidereal dayyear
(yr)____________________

only
needed to calculate V2

Outputs:

V1/∫V2 (cal. factor)

w3dB (corner
freq.)

GHz,
gigaHertzMHz, megaHertzradians/secondHz, HertzkHz, kiloHertzTHz, teraHertzPHz, petaHertzeV, (in
vacuum)____________________

C1 (probe
capacitance)

F,
FaradspF, picofaradsmF,
millifaradsuF, microfaradsnF,
nanofarads____________________

V2
(=RC1dV1/dt)

VoltskilovoltsMegavolts____________________

Output
Format:
top

Select
Format:

Scientific

Engineering

Fixed

Notes:
top

If you know dV/dt then enter 1
second for dt and put dV/dt in for dV1 with volt units (as done for the
default values).

The Vdot probe is essentially a
high pass RC filter with a corner frequency equal to (1/R(C1+C2)) as
shown in the bode plot
below.

Care must be taken to ensure that
the 3dB point is much higher in frequency than the range of
interest.

In most cases, C2>>C1 so
that the 3dB frequency is just 1/RC2

The phase is +90 degrees for low
frequencies, +45 at the 3dB point, and 0 at high frequencies.

For frequencies above the 3dB
point, the probe acts as a capacitive divider.

The values above are from the
design of a typical Vdot probe for Saturn with a center conductor
voltage rising to ~800 kV in about 100 ns.  The peak dV/dt was
estimated from a circuit code.  C2 was calculated from a field
plotting code.  The actual geometry is cylindrical, but the ID is
~6" and OD is ~12" so the approximate planar gap is 6".  The probe
is placed in a recess in the outer conductor so the surface is
flush.  The probe is just a 1.8" diameter disk held in a metal cup
with plastic support.  The output is through an N connector with
center pin attached to the disk as shown below:

Usually, you'll want the peak
output large enough to overcome noise, but much less than the breakdown
strength of the connectors.  Also, the 3dB point is usually desired
to be >500 MHz (the bandwidth of a lot of the scopes).

Copyright ?2006  Raymond J. Allen