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Transcript
```NBE-E4120, Cellular Electrophysiology
Exercise 1
Solving instructions
1. An example solution:
Using trial and error method, we first select a 10M resistor to limit the currents.
Current i divides into two branches, and iin should be ~50 pA. We assume that the
current iin will be small compared to other currents -> i β i2
Letβs try selecting a 100 M resistor to the other branch and then calculating the
resistance for R.
Kirchhoff:
4,5π β π β 10π β ππ = 0
βπ β 10π
ππ β πππ πππ β πππ β 100π = 0
i
10M
iin 100M
i2
R
Rin
2. a) See exercise slides.
b) The difference between the recorded voltage
and the membrane voltage less than 1%:
Combine with the voltage division equation:
π
ππ
> 0,99
π
π
π = π +π
ππ
π
π
β ππ β 50 πΊΞ©
c) Now we start considering signals that change over time. Therefore, we must apply
impedances.
Voltage division for the membrane potential and the measured potential (similar
than in purely resistive circuit):
π=
ππΆ
π
ππ +ππΆ π
1
The impedance of a capacitive component:
ππΆ =
The impedance of a resistive component:
ππ = ππ
πππΆ
The equation that describes the dampening of the signal amplitude as a function of
1
the angular frequency Ο of the signal:
π
π΄=| |=
ππ
β(ππΆ)2
1
β(ππΆ)2 +π2
π
The dampening is given in dB:
β3 ππ΅ = 20 log10 π΄
By combining two previous equations, the angular frequency that is dampened by 3
dB can be solved -> 99,8 1/s, which corresponds to 16 Hz. Does this have an
influence on action potential recording?
3. Noninverting amplifier
βππ = πππ ππ
π
β ππ = (1 + π π ) ππ
ππ
ππ β ππ = ππ ππ
Inverting amplifier
ππ = πππ ππ
π
β ππ = β π π ππ
ππ = ππ ππ
ππ
4. Familiarize yourself with the extra material of lecture 1 (especially chapter
βMeasuring biological signalsβ) and exercise task 2, where you can an example
sketches of recording setups. What have you learned (based on task 2 and extra
material) about e.g. input resistance of a measurement device or the effect of a
micropipette on recording high frequency signals?
```
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