Module 1.2 -- RC Circuits 2024

pdf

School

University of British Columbia *

*We aren’t endorsed by this school

Course

102

Subject

Electrical Engineering

Date

Apr 3, 2024

Type

pdf

Pages

Uploaded by ElderMantis3875

RC Circuits and Cell Membrane Potential Module 1.2: Lab Manual BMEG 102 Biomedical Engineering Laboratory Date: January 30, 2024 Course Instructor: Sukhneet Dhillon 1 Objectives By the end of this lab, you should be able to: • Measure the time constant of an RC circuit using an oscilloscope • Relate measurements for the RC circuit to the change in cell membrane potential to a depolarizing stimulus • Describe the response of an RC circuit in the frequency domain Now that you have completed Module 1.1 and are familiar with using the function generator and oscilloscope, you will proceed with the main experiment of this Module. Note that your team’s lab submission for both Module 1.1 and 1.2 is due February 5, at 11:59 pm . All questions are indicated in bold throughout this manual. 2 Introduction As discussed in lecture, the passive cell membrane can be modelled by an RC circuit. An RC circuit is named after its two components – R esistor and C apacitor – arranged in series. A capacitor is an electrical component that stores electric energy, thereby increasing the capacitance of a circuit. Capacitors are typically constructed by separating two electric conductors (such as metal plates) from one another with a dielectric medium (an electric insulator). When a voltage is applied, as with a battery, current cannot flow through the dielectric

medium. As a result, positive charge accumulates on one conductor while negative charge accumulates on the other conductor, establishing an electric field across the capacitor. Once the applied voltage is removed, the electric energy stored in the capacitor is dissipated in a time-dependent manner. Consider the simple RC circuit in Figure 1, where V o is the constant voltage source. The initial voltage in the circuit at t=0 is therefore V o , and will decrease with time upon instantaneous removal of the voltage source (at time t=0). This change in voltage across the capacitor V(t) with time is described by the following equation: ࠵?(࠵?) = ࠵? ! ࠵? "#/% ࠵?ℎ࠵?࠵?࠵? ࠵? = ࠵?࠵? In the equations above, τ is the time constant of the RC circuit – the value to be measured in your experiments. Consider how you would measure the time constant from a graph of voltage variance with time. Figure 1. Schematic of an RC circuit, a model of the passive cell membrane. This characteristic behavior of RC circuits to discharge (and store) electric energy in a time- dependent manner has been harnessed in various electric devices. Moreover, RC circuits have served as simple models of changes in cell membrane potential. In 1999, Koch et al. injected a constant current into a neuron (a nerve cell) using a micropipette electrode. Upon instantaneous removal of injected current, the cell membrane potential decreased in a manner similar to that observed of an RC circuit. According to this model: • The cell membrane is modelled as a capacitor, an electric insulator that can store electric energy • Ion channels in the cell membrane are modelled as resistors, which allow ions in and out of the cell, but not instantaneously • Ion pumps are like the constant voltage source (or battery), which maintains cell membrane potential

3 Experimental Design: Measuring Time Constant In this lab, your team will use Simulink to design an experiment to study the effect of resistance on the time constant of an RC circuit. Start by building an RC circuit (as shown in Figure 1) in Simulink. Note that the function generator will serve as the voltage source, while the oscilloscope will be used to measure the voltage across the capacitor . Hint: The RC circuit design is similar the to Voltage Divider circuit shown in the pre-lab video . Ensure that the “Voltage Source” block is replaced with the “Pulse Voltage Source” block , as shown in Figure 2 below. Figure 2 . Schematic of voltage source block (left) and pulse voltage source block (right), as used in Simulink. For your lab submission, complete the following activities and answer the questions indicated: Set the Pulse Voltage Source block with a pulse value of 5 Vpp and 50% duty cycle. The square wave will simulate a constant DC current source that is instantaneously turned off. Hint: carefully consider what period (or frequency) is appropriate for your study. Set the “Capacitor” block to a capacitance of 10 μF . • (Rubric component 1) Using your simulation, study three experimental conditions (ie. three different circuit resistances, ranging from 10 kΩ - 50 kΩ). Construct a table that summarizes all of the following elements for each experimental condition: o A labelled schematic of the electrical circuit o The time constant measured using the voltage drop across the capacitor, analysed using the “Cursor” function in “Scope” block in Simulink (reported with uncertainty). o Capture a snapshot of the “Scope” display for each experimental condition. Make sure the horizontal and vertical cursor placements are at the points you used to calculate your time constant

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

• (Rubric component 2) Discuss the following with no more than 400 words ( Hint: to reserve time for the last activity of the lab, outlined in Section 4, you may revisit these questions after the lab session) o Considering the RC circuit as a model of cell membrane potential, what does manipulating the total resistance of an RC circuit represent? That is, what does each experimental condition represent in the model? o Describe a disease that affects the component of the cell membrane discussed above. § What is the cause of the disease (how is it related to the “resistance” component in the RC circuit)? § What tissues and organs are affected, and what are the symptoms? § What cures or treatments are currently available? 4 Frequency Response of RC Circuits In your previous experiment, you studied the RC circuit response to a constant voltage (the square wave was used to simulate instantaneous removal of constant voltage input). However, the frequency domain, where voltage varies with time, is important and equally relevant to real- life applications, especially in signal filtering and electrical noise reduction. In this section, you will be observing the response of an RC circuit to a sinusoidal input voltage with added noise, as represented in Figure 3 below. RC circuits are commonly used in electrical engineering as a filter, to remove unwanted frequencies from an electrical measurement. Figure 3. Schematic of RC circuit with a sinusoidal voltage input. The source input voltage can be described by its constant amplitude V o and frequency ω, according to the following equation: ࠵? !" (࠵?) = ࠵? # cos(࠵?࠵?) However, as with all electrical signals, there will be some amount of electrical noise in our measurement. Therefore, our source voltage can be further characterized by the noise amplitude V in and frequency ω n , according to the following equation:

࠵? !" (࠵?) = ࠵? # cos(࠵?࠵?) + ࠵? " cos (࠵? " ࠵?) For the last part of your lab submission, complete the following activities and answer the questions indicated: Download and open the Simulink file “Module1_FR” from Canvas. • (Rubric component 3) Vary the value of the capacitor, without changing other parameters of the source. Measure the resulting voltage amplitude across the capacitor. Use a table to record a minimum of 5 measurements for your lab submission (ie. for 5 different capacitance values. Peak-to-peak voltage amplitude can be measured using the cursor measurement tool in the “scope” block (Figure 4). Measure the resulting peak- to-peak voltage amplitude across the capacitor). You should notice that different capacitor values reduce the electrical noise amplitude to different degrees, but also reduce the amplitude of the primary signal. Be sure to measure more data points in regions where you observe large changes in amplitude. Include a label of the table above the table itself, in the form “Table 1. Enter short description of the table.” • In your table, find the capacitor value which is most effective at reducing the noise while also preserving the original 5V amplitude electrical signal (reduction in amplitude < 20%). Using your chosen capacitor value, plot the original signal and the filtered signal on the same plot in MATLAB . Ensure that figure axes are properly labelled and that a figure legend is included. • (Rubric component 3) From your data and observations, what is an important function and application of the RC circuit in electronics? Use a maximum of 200 words. Incorporate the term “low-pass filter” into your response.

Figure 4. Electrical signal with added noise. Green highlight shows the cursor function. Peak-to-Peak Amplitude

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version