S-Plane of passive filter with charge input

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Hi,

I have a problem in that I need to calculate the S-Plane TF for a
bandpass filter that has a charge input from an accelerometer. The
simple circuit is as follows.



-----------------C1uF---------------------------
R475-----------------
| |
| |
q_in R1M R1M C220nF C10nF q_out
| |
| |

------------------------------------------------------------------------------

And a copy just in case it does not line up right!

-----------------C1uF---------------------------
R475--------------------------
| |
| |
q_in R1M R1M
C220nF C10nF q_out
| |
| |

------------------------------------------------------------------------------


Where q_in is the input from the accelerometer (at 17.5pC per g). The
q_out then goes to an op amp charge amplifier where it is 'converted'
to a voltage by a 4.7nF feedback capacitor so that Vout of charge amp
= q_out/4.7nF

The question is how do I relate q_in to q_out as an S-Plane transfer
function, as I need to know the frequency response of this circuit as
it is compensated for later in the signal path, and also for a test
calculation. SPICE simulations have been done for the whole circuit,
and this circuit section has a high pass cutoff of ~1Hz and low pass
of ~1450Hz. Why does it appear that the R1M, C1uF and R1M form the
high pass, and C220nF, R475 and C10nF form the low pass part?

I know that for charge analysis in the S-plane, R -> SR and C -> 1/C,
but I can not work this out.

I hope someone can shed some light.

Thanks,

Lee.

 

[JosephKK]

On Thu, 25 Sep 2008 07:12:52 -0700 (PDT),

Hi,

I have a problem in that I need to calculate the S-Plane TF for a
bandpass filter that has a charge input from an accelerometer. The
simple circuit is as follows.



-----------------C1uF---------------------------
R475-----------------
| |
| |
q_in R1M R1M C220nF C10nF q_out
| |
| |

------------------------------------------------------------------------------

And a copy just in case it does not line up right!

-----------------C1uF---------------------------
R475--------------------------
| |
| |
q_in R1M R1M
C220nF C10nF q_out
| |
| |

------------------------------------------------------------------------------


Where q_in is the input from the accelerometer (at 17.5pC per g). The
q_out then goes to an op amp charge amplifier where it is 'converted'
to a voltage by a 4.7nF feedback capacitor so that Vout of charge amp
= q_out/4.7nF

The question is how do I relate q_in to q_out as an S-Plane transfer
function, as I need to know the frequency response of this circuit as
it is compensated for later in the signal path, and also for a test
calculation. SPICE simulations have been done for the whole circuit,
and this circuit section has a high pass cutoff of ~1Hz and low pass
of ~1450Hz. Why does it appear that the R1M, C1uF and R1M form the
high pass, and C220nF, R475 and C10nF form the low pass part?

I know that for charge analysis in the S-plane, R -> SR and C -> 1/C,
but I can not work this out.

I hope someone can shed some light.

Thanks,

Lee.

First, the output of the charge amp is in volts/g at audio
frequencies.

Unless you are rolling your own charge amplifier please use this
simplified response model:

Flat except for 2nd order LF rolloff with knee at about 1 Hz and 1st
order rolloff at about 200kHz.

Finally, you MUST use special accelerometer cable assemblies, just buy
the very expensive things and coil up the slack. It has been over 20
years and my hands are not up to installing the connectors, and i
don't have the expensive jigs, and the cable itself is pretty pricey
special stuff.