Biological Sciences 300/301, Smith College | Neurophysiology
Lab 2: Circuits and Amplifiers
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Our goal today is to work with simple electrical circuits to develop insights into electrical potentials (voltages) and currents. Throughout, there will be examples of how the concepts are applied in neurophysiology. We will also learn about the preamplifiers that we will use for future experiments.
1. Ohm's Law
We'll begin by observing Ohm's Law in circuits involving several resistors. Ohm's law says that when a voltage (an electrical "push") is applied to a circuit, the amount of current that actually flows through the circuit is inversely proportional to the total resistance the circuit offers. More resistance means less current:
E = I x R
volts = amps x ohms
Another law says that in a circuit, current can't pile up or disappear. The current flowing through every point in series in a circuit is the same. Consider this circuit:
The same current, I, flows through both resistors. Resistors in series add up, so in our circuit, the total resistance is 15,000 ohms. The voltage is 1.5 volts. By Ohm's Law, the current is
1.5 volts = I x 15,000 ohms
I = 1.5 / 15,000 = 10-4 amp = 0.1 milliamp
The total voltage of 1.5 volts is "used up" in pushing current through the two resistors. Most of the voltage is used pushing charges through the larger resistor. The voltage across either resistor can be calculated using Ohm's Law:
That is, 1.4 volts is used in forcing current across the big resistor, and only 0.1 volts is used across the small resistor.
Experiment: Measure the voltage across resistors in series for yourself. We have soldered two resistors together: 1000 ohms and 10,000 ohms (use the color code below to identify them). Set up this circuit with a 6-V battery and clip leads:
A word about polarity:
An isolated circuit of a battery and resistors does not have any point defined as zero (ground). When you attach a clip lead connected to ground, that point becomes defined as zero volts. Other locations in the circuit then take their relative positions with respect to zero. For example, if you ground the negative pole of the battery, that pole becomes zero and the other pole becomes +6 volts. If you ground the positive pole instead, the other pole becomes -6 volts. The oscilloscope trace will step up in the first case and down in the second, but the step will be 6 volts big in either case.
Use your oscilloscope to measure the voltage across each element of the circuit. Set the oscilloscope's
- channel 1 coupling on DC
- vertical sensitivity at 2 V/div
- vertical position at midscreen
- sweep on 1 msec/div (to get a straight line)
- trigger on auto mode.
Attach a BNC/double-banana cable to channel one. Place a clip lead on each "banana" of the double-banana plug, and then attach the free ends of the clip leads on either side of various components. Measure the voltage and calculate the current for each component. Is the current the same in each part of the circuit?
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measure voltage: |
volts (measured) |
current (calculated) |
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across both resistors together |
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across the small resistor |
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across the large resistor |
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Disconnect the battery when you are through.
Application: The principle that a voltage divides across resistors in series is important when recording with microelectrodes. These have very high resistances of 10 megohms (107 ohms) or more due to their very small tips. The microelectrode's resistance is in series with the input resistance of the amplifier, and the potential in the cell divides across the two resistances. Here's the circuit:
The amplifier can only detect the potential that appears across its input resistance. Any potential drop across the electrode is "lost." For example, if a cell's resting potential is -100 mV and the electrode and amplifier have equal resistances, the potential would divide equally across the two resistances. The cell would appear to have a resting potential of only -50 mV. To prevent this artifact, the amplifier's input resistance must be huge compared to the electrode's resistance. Amplifiers used with microelectrodes typically have an input resistance of 1012 ohms.
Problem: Estimate the proportion of the "real" potential that will be lost across a 10-megohm electrode if the amplifier's resistance is 1012 ohms. Would you consider the measurement error negligible?
2. Resistors and capacitors together.
A capacitor is a device that stores electric charge. Cell membranes are capacitors, and electronic circuits often have capacitors made of two thin sheets of metal foil with an insulating sheet between them, rolled up into a small cylinder. The amount of charge stored in a capacitor is proportional to its capacitance, C. The units of capacitance are "farads," but typical capacitors are in the microfarad range, and capacitances are routinely given in µF (10-6 F).
If a capacitor is connected to a battery as in the circuit at the left, electric charge will flow out of the battery as fast as it can until the capacitor is storing all the charge that it can hold. At this time, the flow of charge will cease, and the voltage across the capacitor will equal the voltage of the battery. The capacitor will continue to hold the charge indefinitely, even if the battery is disconnected.
Inserting a resistor in the circuit changes only one aspect. The rate at which charge flows out of the battery will now be limited by the resistor. Instead of charging up instantaneously, the capacitor will require some time to obtain all the charge that it can hold. During this charging time, the voltage across the capacitor will increase, starting at zero when the circuit is first connected, and reaching the voltage of the battery when the capacitor is fully charged.
Time constant: The time the capacitor requires to reach full charge depends on both the size of the resistance (big R means slow flow of charge, which means it takes a long time for the full charge to accumulate), and the size of the capacitor (a large capacitor holds more charge, so it takes longer to accumulate all the charge it can hold). The charging rate is exponential, and the time required to reach 63% (= 1 -1/e) of the full voltage applied is defined as the time constant of the circuit. The time constant (in seconds) is equal to the resistance (in ohms) times the capacitance (in farads). The time to discharge 63% is also equal to the time constant.
Time constant
TR=RRRxRC
(sec) (ohms) (farads)
Experiment: Observe the charging of a very large capacitor. We will use electrolytic capacitors, which require that one terminal (marked with a red dot or a +) be connected to the positive side of the circuit. Always be careful to observe this polarity. Clip together the following circuit except for the battery, which you should not connect until you are ready to observe the voltage across the capacitor.
Set the oscilloscope on Roll mode by holding down the "Norm" and "Hold" buttons simultaneously. You may wish to adjust the horizontal position of the trace so that you can see the right end of the displayed line, where new points are added.
Note that in roll mode, only the four slowest sweep speed settings are permitted, and they must be interpreted as if they were multiplied by 100. For example, if the time/div knob points to 20 msec/div, in roll mode it becomes 20 msec/div x 100 = 2000 msec/div (= 2 sec/div).Any setting faster than the four permitted settings behaves like the fastest of the permitted settings, 2 sec/div.
Click image for more detail.
Briefly connect a wire between the capacitor's two terminals to guarantee that the capacitor is fully discharged. Then connect in the battery and watch the voltage across the capacitor slowly increase as charges pile up on its plates. When the capacitor is fully charged, disconnect the battery. The charge on the capacitor remains, and the voltage across it will stay the same.
Discharge the capacitor while observing the voltage by connecting together the two wires that formerly went to the battery:
Discharging is the inverse situation from charging. The capacitor slowly loses charge at a rate limited by the resistor till the voltage across the capacitor reaches zero.
Measure the time constant of the resistor-capacitor circuit. Set the vertical sensitivity at 1 V/div. The trace will step up 6 divisions from the zero baseline when the capacitor is fully charged. Simplify your estimate by treating 63% as approximately two-thirds (66%), or four vertical divisions up from zero.
Charge the capacitor. Freeze roll-mode (by pressing hold) when the capacitor is fully charged, but before the zero-volt baseline has slid off the screen. Position the trace horizontally and vertically (make these adjustments after the trace is on hold) so that charging begins at the intersection of two major graticule lines. Count up four vertical divisions from zero, and measure the time (horizontal divisions) between the start of charging and the moment when the trace crosses the two-thirds line.
Calculate the capacitor's capacitance using the formula for the time constant. Substitute the values of the resistor you used and the time to two-thirds charge that you measured. Does your calculation agree with the value printed on the capacitor (within the precision of our rough methods)?
Replace the resistor with one of approximately twice the resistance (2200 ohms), and charge the capacitor again. It should now reach full charge more slowly as the larger resistor further limits the flow of charge in the circuit. Measure the time constant for this resistor, and again calculate the capacitance. Does the calculation agree with your previous one?
The capacitor-resistor circuit will be used again in the next section.
Application: When a voltage pulse is introduced in a nerve cell (either naturally, at a synapse, or experimentally, through an electrode), the shape of the voltage pulse gets lower and "rounder" as one records at greater and greater distances from the pulse's starting point. What one is seeing is the charging of a capacitor: in this case, the capacitor formed by the lipid bilayer of the membrane sandwiched between conducting solutions on each side. A famous model of an axon's resistance and capacitance is shown below. The axon membrane is represented as a series of resistors and capacitors, and the solution on each side as a series of resistors. The circuit is basically similar to the one you just put together.
Measuring current in a resistor-capacitor circuit. Suppose in the previous circuit we had measured the current flowing across the resistor instead of the voltage across the capacitor. We would have seen a large current flowing initially, when the capacitor was empty, and very little current flowing later, as the capacitor became more fully charged. When the capacitor reached full charge, the current flow would become zero.
We can qualitatively measure the current flow in a circuit by measuring the voltage across a resistor. (The actual value of the current can be calculated if we know the value of the resistor.) Ohm's law states that the voltage across a resistor is equal to the current times the resistance. A large measured voltage means a large current, and a small voltage means a small current.
Experiment: Adapt the circuit in the previous experiment to measure current by connecting the oscilloscope across the resistor rather than across the capacitor. Use the same resistors and big capacitor as before, and again make your observations using roll mode.
When you connect the battery, you will see its full voltage across the resistor, as only the resistor limits the flow of current. As the capacitor continues to charge, the charges accumulating on its plates tend to repel the new charges arriving. Current in the circuit flows ever more slowly, and as less current flows, the voltage across the resistor (I x R) becomes smaller and smaller. Eventually, when the capacitor is fully charged, no current flows, and the voltage across the resistor becomes zero (0 x R = 0).
When the capacitor is discharged through the resistor, the same situation occurs in reverse. Currents that flowed in a particular direction when charges were travelling to the capacitor now flow in the opposite direction as charges move away from the capacitor. During discharge, the voltage transient representing current flow across the resistor has the same shape but the opposite sign as it had during charging. Charge and discharge the capacitor circuit several times to observe this yourself.
Application: One reason for understanding resistor-capacitor circuits is that many amplifiers are built with a "coupling" capacitor in series with the input resistance. The amplifiers are called "capacitor-coupled" or "AC" amplifiers. The DAM-50 amplifiers that we will use in future weeks can be either capacitor coupled (AC) or direct coupled (DC), depending on the setting of a front panel switch.
Our oscilloscopes also can be either AC or DC coupled, depending on the setting of the AC/GND/DC switch for channels 1 and 2. The circuit diagram for the oscilloscope's input stage is shown below.
The section in the blue square shows the front-panel BNC input connector for channel 1 with a wire leading to the AC/GND/DC switch. The switch is represented as three open circles, one above the other, with an arrow from another circle just to the right. You are meant to understand that the arrow can point to any one of the three open circles, depending on the switch setting. For a larger, labelled image, click the figure.
The path from the BNC connector to the input preamplifier can lead across a capacitor (top position, the AC setting) or go directly with no capacitor (bottom position, the DC setting). In the middle (GND), the input signal just "hangs" there, and the preamplifier is connected internally to ground.
Experiments: The oscilloscope's AC setting is like the circuit you just worked with. Use a slow sweep speed (not roll mode), and set the channel's input switch to DC. Connect a battery to the oscilloscope. The trace will step up in a square pulse, and the voltage will persist until you disconnect the battery.
Now set the switch on AC, and again connect the battery. You will see a transient deflection of the trace that rapidly returns to baseline even though the battery is still connected. The transient is very fast because the capacitor in the circuit is much smaller than the one used in your experimental circuit.
Disconnect the battery and quickly touch the oscilloscope's input wire to ground to discharge the internal capacitor. You will see a transient of the opposite polarity, just as you did in your experimental circuit. Current flows in the opposite direction when the capacitor discharges.
Why would anyone ever build a capacitor-coupled circuit? We have just seen that capacitor-coupled (AC) circuits distort signals, eliminating steady voltages and preserving only rapid changes. Why would anyone accept a distorted signal? The answer is that an AC-coupled circuit is simpler to design because it is very stable (the baseline voltage never drifts away from zero), and in applications where steady voltages are not of interest, AC amplifiers are actually better. When we record action potentials with extracellular electrodes, we will use AC coupling for the preamplifier and the oscilloscope. Action potentials are very brief, and AC circuits reproduce this transient voltage accurately. Since the baseline voltage is of no special interest for extracellular recording, nothing is lost by using an AC amplifier. (On the other hand, resting potentials and slow generator potentials do require direct-coupled DC circuits, since these signals contain steady or slowly changing components that would be filtered out by AC circuits.)
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3. Preamplifiers for extracellular recording.
An action potential recorded extracellularly is a very small electrical change, typically tens or hundreds of microvolts. This would not be visible on our oscilloscopes even at their maximum vertical sensitivity. Consequently, a preamplifier is used between the electrodes and the oscilloscope. Typically, a preamplifier for extracellular recording has an amplification factor ("gain") of about 1000x.
Because the amplification factor is so large, any stray signals that are picked up by the electrodes or the wires (which act like antennas) are also amplified and can turn out to be quite substantial. The major sources of stray signals are the AC power lines and the room lights, both of which broadcast 60-cycle electrical interference. Neurophysiologists try to shield their experiments from electrical noise by using grounded baseplates, shielded cables (where a grounded wire braid intercepts the electrical noise), and differential preamplifiers.
Differential inputs. A differential preamplifier has two active inputs plus a ground (rather than just one active input and a ground, like most amplifiers). The amplifier inverts one of the two inputs and adds it to the other input. This is equivalent to subtracting one input signal from the other. Any noise component that is common to both signals is subtracted out, leaving the difference between the two signals for further amplification (hence the name "differential" amplifier). The amplifier's output is "single-ended", with one active wire and a ground.
In recording neural activity with a differential amplifier, one uses two electrodes and arranges the wires from them so that they are the same length and run next to each other. The two wires will pick up the same electrical noise, while the biological signals on them will be different. The output provides an amplified biological signal with most of the electrical noise subtracted.
On the input block of our DAM 50 preamplifiers, the red input post is the non-inverting (A) input, the black post is the inverting (B) input, and the white post is ground. It is customary to connect the active electrode to the non-inverting input (red), and to connect the reference electrode to the inverting input (black). In this arrangement, when the preamplifier is connected to the oscilloscope, a positive voltage at the active electrode will produce a positive (upwards) signal on the oscilloscope screen.
Filtering the signal. As mentioned above, our preamplifiers have coupling capacitors on their inputs. These serve to block steady and slowly changing (low frequency) signals, allowing only quick transients to come through. We have already seen that if a capacitor is very large (like the big one we used in our test circuits), moderately slow transient signals will get through. If the capacitor is small (like the one that AC-couples our oscilloscopes), only very rapid transients get through. Different sized capacitors create different degrees of filtering.
Any electrical signal may be thought of as the sum of components of many different frequencies. For an action potential, the important components are around 1000 cycles per second (1 kHz). Riding along with this may be unwanted components such as low-frequency drift (below about 10 Hz), power-line noise (60 Hz), and high-frequency electron noise (above 10 kHz). By selecting appropriate coupling capacitors, some or all of the unwanted frequencies can be filtered out.
Our DAM 50 preamplifiers have adjustable low-frequency and high-frequency filters. The filter settings are identified by the frequency of the signal that is reduced to about half its actual amplitude. For example, a low-frequency setting of 10Hz means that signals of 10 Hz are reduced to half their real amplitude, signals below 10 Hz are reduced even more, and signals above 10 Hz are reduced less or not at all. High-frequency filter settings also are named for the frequency that is reduced to half its real amplitude, but it is the frequencies above the setting that are reduced more.
Filter Settings on DAM 50 Preamplifiers: The graph below shows the relative amplification plotted against the signal frequency for a DAM 50 preamplifier that has its low-frequency and high-frequency filters at various settings.
The data were obtained by connecting a sinewave generator to the preamplifier's input. The sine wave amplitude was always 40 mV peak to peak. The amplifier's gain was set at 100, and the coupling mode was AC. The output signal was measured for a series of test sinewave frequencies between 5 Hz and 10 kHz (horizontal axis, a logarithmic scale). For each test frequency, either the low-frequency filter was set to each of its possible values (0.1, 1, 10 or 300 Hz) with the high-frequency filter at its least restrictive value (10 kHz), or the high-frequency filter was stepped through its possible values (100 Hz, 1 kHz, 3 kHz, 10 kHz) with the low-frequency filter at its least restrictive value (0.1 Hz). At each setting, the output signal was measured, and the amplification was calculated and plotted as a fraction of the maximum amplification.
The low-frequency filters reduce the amplification at the left (low) end of the frequency range. The high frequency filters reduce the right (high) end. The frequency range that remains for any combination of high- and low-filters is the middle zone between their two curves. For example, the arrow shows the span of frequencies that would remain with the low-frequency filter set at 10 Hz and the high-frequency filter set at 1 kHz.
In practice, both the high- and low-frequency filters are set by trial and error. The trick is to adjust the filters to block out distracting components of the signal (for example, low-frequency baseline drift and high-frequency electronic hiss) without reducing components of interest. Since action potentials have a major signal component at about 1 kHz, we have to be careful not to drop the high-frequency filter below its 1-kHz setting, or we will distort or even eliminate completely the action potentials that we are trying to see.
True story: Occasionally, a lab group thinks that they have not managed to get an experiment to work successfully, only to discover that they actually were getting excellent recordings, but were inadvertently filtering out the spikes.
Experiment: Check the filtering and amplification of your DAM 50 preamplifier.
Use the 0.5V CAL (calibration) signal on the oscilloscope's front panel for this test, but be careful. The 0.5V signal is very big to feed directly into the preamplifier, which was designed to accept signals of a few microvolts or millivolts (0.5 volts is 500,000 microvolts!). Luckily, if the DAM 50 mode is set on DC coupling, then the amplification (gain) can be set on 10x, which is low enough to keep the amplified signal within a safe range.
CAUTION:
Find the mode and gain controls on the DAM 50, and set them to DC mode and 10x gain before you do anything else. You risk damaging the amplifier if you are careless about this step.
Place the oscilloscope in two-channel (chop) mode. One channel will be used to look at the signal going into the amplifier, the other to look at the signal coming out.
Connections:
Use a BNC/double-banana cable to connect channel 1 to the DAM 50's red and white input terminals. (White is ground; check the tab on the double-banana plug.) Channel 1 will show you the signal you put into the DAM 50.Use a BNC/BNC cable to connect channel 2 to the output of the DAM 50. Channel 2 will show you the amplified output signal.
Set the DAM 50's input selector on A. The coupling mode should already be DC and the gain 10, as stressed above. Use a clip-lead to connect the CAL tab to the red input plug of the DAM 50.
Turn on the amplifier's power, and adjust the oscilloscope's controls until the input and output signals are big and easy to see on the screen.
Measure the amplification. Set the high-frequency filter set at 10 kHz. Measure on the oscilloscope screen the amplitude in volts of the signal going into the amplifier and the signal coming out. Calculate the amplification factor (gain). What did you expect the gain to be? What is it actually?
Observe high-frequency filtering. Start with the high-frequency filter set at 10 kHz, the least restrictive setting. Reduce the high frequency limit in steps while looking at the screen. Can you make sense of the distortions introduced by filtering out the high frequencies? (Remember that the quick up-down portions of a square wave represent the highest-frequency components of the signal. When they are filtered out, the square wave starts to look rounded.) What is the lowest high-filter setting that you could use for the CAL signal without introducing unacceptable distortion?
(For the curious, we can't test the effects of the DAM 50's low-frequency filter with this CAL signal because we need DC coupling to get 10x gain, and the low filter is not in the circuit for DC coupling.)
Links
Appendix: Cables and Connectors.
Appendix: DAM 50 Preamplifier
© 2003 by Richard F. Olivo. Permission is granted to non-profit educational institutions to reproduce or adapt this Web page for internal use provided that the original source and copyright are acknowledged.