TEC-B-01 User Manual
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version 1.1
page 33
The speed of response (with x1 headstage and 150 V output) from the point of view of control theory
is:
T
r
= 94 µs
T
s
= 168 µs
Maximum speed of response
The speed of an ideal VC system is limited only by the maximum current delivered by the current
source:
[dUm/dt]
max
= U
max
/ (C
m
*R
EL
)
[dUm/dt]
max
= 150 V / (0.1 µF * 1 M
) = 1500 V / s = 1.5 mV / µs
It would last 100 µs to reach 150 mV, provided that the clamp has an ideal characteristic.
Now the minimum bandwidth of a real clamp system necessary for "ideal" behavior can be calculated:
T
s
= 8.4 * T
e
= 100 µs gives T
e
= 12 µs; BW = 1 / (2 *
* Te) = 13 kHz
with BW = bandwidth
If we assume that T
e
is determined by 70 - 80% by the time constant of the current electrode (i.e. T
el
=
10 µs if T
e
= 12 µs) it is clear that with electrode resistances in the range of 500 k
the total capacity
related to the current injecting electrode can be maximum 20 pF. In this case the maximum cable
length is 15 - 20 cm.
A cable of 0.5 - 1.5 m has a capacity in the range of 50 - 200 pF. With such a capacity and an electrode
resistance of 1 M
, T
e
is in the range of 50 - 200 µs and the speed of response would be in a range of
0.5 - 2 ms!
Conclusions:
1.
For adequate VC experiments a clamp gain of 1 - 5 mA / V (i.e. 100 - 500 internal gain with a
current source calibration of 10 µA / V) is necessary. Therefore, with pulse amplitudes of 100 -
200 mV the operational amplifiers in the gain stages will be saturated causing nonlinear
components in the capacitive transients.
2.
The maximum speed of response is determined by the cell capacity, the maximum available
current and the command amplitude.
3.
The real speed of response is determined by the time constant associated with the current
injecting electrode. It is strongly dependent on the length of the cable that connects the
headstage with the electrode holder.
Important
: The speed of response and the linearity of the capacitive transients can be improved
considerably if a current headstage with a steeper gain (x2 = 20 µA / V, x5 = 50 µA / V) is used
especially in combination with a higher output voltage of ±225 V (TEC 225 System) and an improved
series resistance compensation (Dietzel et al., 1992; Polder and Houamed, 1994; Greeff and Polder,
1997; Greeff and Kühn, 2000).
