Exercises Day 2: No Hardware#

1. Capacitor and Resistor in parallel#

In the circuit below, you will see a capacitor and a resistor in parallel. The voltage source alternates at 20Hz, going from -10 to +10 volts. The current travels over the resistor or via the capacitor to ground.

../../_images/cap_res_parallel_sim.png

Exercises

1A. Increase the value of the resistor to 200kOhm. What happens to the current through the resistor?

1B. Put the resistor back to 10kOhm. Now, increase the capacitance of the capacitor to around 10mF. What happens to the current?

1C. Return the values to 10kOhm and 100nF.

Change the frequency of the alternating signal to

  • 1000 Hz (action potentials!)

  • then to 1 Hz

You may have to change the simulation speed using the red slider at the top right, and adjust the x-scaling of the scope below (right-click / properties / and slide the ‘horizontal scale’).

How does the frequency of the signal relate to how much current crosses either the capacitor or the resistor?

2. The equivalent circuit of the electrode#

In the theory handout, we discussed how we can represent an electrode as a circuit containing a resistance and a capacitance. We’ll now build this equivalent circuit in the simulator.

Exercises

2A. In the simulator, edit the circuit used above to build the equivalent circuit of a polarised, tungsten electrode. See the theory handout for more details.

Here are some values to use:

  • Rm: the DC resistance of the metal electrode wire, 10-100 Ohms.

  • Ce: the electrode tip capacitance, generated by the double layer generated around the electrode. Ce ~ 0.2 pF / µm2, so 10 - 20 pF (if the electrode is unplated)

  • Re: electrode tip resistance, in parallel with Ce. ~ 100 MOhm.

  • Edit the alternating voltage supply to provide 1V at 1Khz, mimicking the signal coming from your cell. 1V is larger than ephys signals, but makes the current flow easier to see. Change the sliders for simulation speed and current speed until you can see where the current is flowing.

2B. What happens if you delete the resistor Re?

2C. Bonus exercise: Can you change this circuit from a polarising, tungsten electrode, to a circuit representing a nonpolarizable electrode?

3. Shunt Impedance#

Here is the circuit of the electrode with a shunt impedance added of 100 pF:

../../_images/day2circuit.png

Exercises

3A. What is shunt impedance here?

3B. What % of our signal are we losing between Vec and Vin? Why?

3C. What could we change to increase the signal at Vin?

3D. The tips of certain electrodes, e.g. nichrome tetrodes, can be electroplated in a thin layer of gold. This ‘goldplating’ increases the surface area of the tip, creating more space to separate charge. This increases tip capacitance by around 100x. Make this change in the circuit simulator. How similar are Vec and Vin now?

Recording Circuit#

To actually perform a recording, we will have to attach the electrode to the rest of an acquisition system. The recording system has an analog to digital converter (ADC), and a recording computer. The leakage resistance here is where the recording system is connected to ground.

../../_images/day2withac.png

Exercises

3E. How much of the voltage at the electrode, Vec, are we recording at Vout?

3F. Add a headstage to this circuit, by placing an ideal operational amplifier between the electrode and the long wire. What happens to Vout? Why?

3G. Change the circuit to stop the amplifier from saturating. What is the amplifier gain now?

4. Operational Amplifiers#

Voltage rails#

In the simulator, ‘ideal’ operational amplifiers are shown without their power supplies. However in real life, we need to provide our op-amp with power. We will use batteries to make voltage ‘rails’. We are going to make a -3V and +3V rail using simulated AA batteries that provide 1.5V each.

To do this we use a common trick and turn two regular power supplies into a bipolar power supply.

../../_images/bipolar_power_supply.png

Exercises

4D. Using 4x 1.5 DC voltage supplies simulated batteries, connect them together so that you have a +3, 0, and -3 power supply.

../../_images/aa_batteries_sim.png

4E. Replace the ‘ideal’ op-amp with a ‘real’ op amp in the simulator. Use a bipolar power supply to power it. What amplitude values do you get as output now? How is it different to the ideal op amp?

Bypass capacitors#

Bypass capacitors are small capacitors that act like little secondary batteries. The batteries we use have a high ESR - ‘equivalent series resistance’, and some capacitance. This means that are not great at quickly providing current. Because of this, when our op-amp starts working, it can run out of current for a very short time until the battery can drive the rails back to their original voltage. This is bad for the signal quality.

So, we allow these small capacitors to charge. If the battery briefly can’t provide current, the bypass capacitors will discharge, providing quick back-up current. We’re exploiting the fact that these caps have very low ESR and can provide current pretty much instantaneously. The fact that they’re too small to power anything for more than a millisecond does not matter here, at that point the batteries have caught up.

Exercises

4F. Add bypass capacitors to the simulation based on where they are in the bipolar power supply pictured here:

../../_images/fritz_bipolar_power_supply.png