Lecture 2-1. Basic circuit elements

Yoonkey Nam

How do we use circuit models

in bioengineering field?

Excitable cell membrane model

3

Core-conductor model: ‘axon’ model

Electrical model for single excitable fiber

4

Electrical stimulation of excitable cells

5

Electrode model: Electrode-tissue interface

6

Instrumentation systems

7

Sensor Analog circuits

Analog-to-digital converter (ADC)

Digital signal processing (DSP)Display

Data storage

LAN

Control & Feedback

Biological system

Body

Tissue

Cell

Biomolecules

Digital-to-analog converter (DAC)

Instrumentation for ‘measurement’

sensor

signal amplifier

signal filter

DSP / Display

Brain / neurons

DAQ

Instrumentation for ‘stimulation’

actuator

nerve tissue

Electric signal generator

Both cases (measurement & stimulation) can be further generalized

sensor

signal amplifier

signal filter

computer display

Brain / neurons

actuator

nerve tissue

Electric signal generator

Try to divide into two parts ...

Two big parts: Source vs. Load

signal or energy generating or supplying

parts

signal or energy receiving or consuming

parts

signal or energy flow

Can you model the following cases with sources and loads?

Bioinstrumentation model Source vs. Load

signal or energy generating or supplying

parts

signal or energy receiving or consuming

parts

signal or energy flow Pulse

generator (source)

nerve tissue (load)

Some examples

• Signal source and receiving or processing load

- Voice amplifying microphone system

- In ECG monitoring system, body is a ECG signal source and

amplifier/filter and display units are signal processing load

• Energy source and consuming load

- MP3 player circuits and battery

- Power plant and buildings

- Beating heart and blood vessel network

- In DBS system, electrical pulse generator is delivering

sufficient electrical energy (‘source’) to the surrounding nerve

tissues (‘load’) which consumes the energy

Electronic devices and their symbols

Actives

Passives

Sources

Discretes

Independent sources Provide current or voltage independently

Voltage source

Current source DC source AC source

These are popular symbols

Loads:  Receive  voltage  or  current  signals  and  consume  energy

17

Can  you  name  these  ?  Do  you  know  how  they  look  like?  

A generic two-terminal network element

Terminal 1

Terminal 2

i(t)

v(t) = v(terminal 1) - v(terminal 2)

+

-

Two ‘measurable’ quantities

Voltage Current

€

v(t) =dUdq

€

i(t) =dqdt

1 V = 1 J/C 1 A = 1 C/sec

Energy per unit charge Flow rate of electric charge

Conservation of charge

i1(t) i2(t)

i1(t) = i2(t)

No net charge accumulation

Voltage and current sign convention

i(t)

+ !

v(t) !

-+ 3A

a

b

+ 3A is flowing from a to b

= - 3A is flow from b to a

Remember the sign convention

Remember the sign convention

i(t)

+ !

v(t) !

-

a

b

vab = + v(t)

iab = + i(t)

If you write the voltage between a and b as

then the resulting current convention should be

v - i characteristics

Every circuit element impose some kind of

constraint between v(t) and i(t)

resistor (R)

capacitor (C)

inductor (L)

€

v(t) = R × i

€

v(t) =1C

i(t)dt∫

€

v(t) = L didt

More complicated devices Transistor: Three terminal device !

+ VCE

-

(Collector)

(Emitter)

(Base)

VBE

+

-

IC

IE

IB

IC = β IB

IC = α IE

VBE > 0.7 (V)

(Collector)

(Emitter)

(Base)

First, define v and i Second, write a device equations

Circuit elements, symbols, v-i relation

Resistor

Inductor

Capacitor

+ -

+ -

+ -

€

v(t) = R × i(t)

€

v(t) = L didt

€

i(t) = C dvdt

Resistance

v(t)

i(t)

€

v(t) = R × i(t)

Resistance R: ohm [Ω] “line slope”

Conductance G = R-1 [S]

For a given cross-sectional area(A), length(L), and resistivity(ρ), what is R ?

Resistor

28

Figure  2–24            Typical  fixed  resistors.

Figure  2–27            Typical  wirewound  power  resistors.

Figure  2–35            Typical  potenDometers  and  two  construcDon  views.

Variable  resistors

Why  do  we  need  a  variable  resistor?

Inductance

Current flow(i) at a coil induces flux(ψ) by magnetic field

ψ(t) = L x i(t)

L (inductance) : Henry [H]

€

v(t) =ddtψ(t) = L di

dt

When ‘time-varying’ current is applied, non-zero voltage can be induced

i(t)

+ !

v(t) !

-

Understanding the voltage drop at inductor

• Inductor is made of a ‘metal’ wire

• Ideal metal has zero resistance (R = 0)

• For any constant current (i), v = R x i = 0

• It is not possible to have non-zero voltage at the inductor except the following special case:

• Time VARYING CURRENT flow!

• v = L x (di/dt)

• Time varying current(i(t)) will make non-zero v!

• Most common time-varying current is sinusoids: i(t) = A cos(wt)

Inductor

32

Figure  14–7            Some  common  types  of  transformers.

Capacitance

i(t)+ !

v(t) !-

€

i(t) =ddtQ = C dv

dt

€

C =QV

How much charge can be accumulated at a parallel metal plate separated by a dielectric, when a voltage is applied?

When ‘time varying’ voltage is applied, non-zero current can flow

Understanding the current flow at capacitor

• Capacitor is made of two metal plates ‘separate’ by insulating materials (dielectric material such as air)

• Ideal dielectric material has infinite resistance

• For any constant voltage (v), i = v / R = 0

• It is not possible to have non-zero current at the capacitor except the following special case:

• Time VARYING VOLTAGE!

• i = C x (dv/dt)

• Time varying voltage(v(t)) will make non-zero i!

• Most common time-varying voltage is sinusoids: v(t) = A cos(wt)

Capacitor

36Figure  9–12            Basic  construcDon  of  axial-­‐lead  tubular  plasDc-­‐film  dielectric  capacitors.

1  pF  ~  0.1  μF  100  V  ~  2500  V  (dc)

εr  =  5.0

Figure  9–8            ConstrucDon  of  a  typical  radial-­‐lead  mica  capacitor.

Less  than    1  μF  (typical)  Max  100  μF

Mica  capacitor

PlasDc-­‐film  capacitor

polycarbonate,  propylene,  polyester,  polystyrene,  ...

εr  =  1200  1  pF  ~  2.2  μF  Max  6000  V  (dc)

Figure  9–10            Examples  of  ceramic  capacitors.

Ceramic  Capacitors

Electrolyte  Capacitors

Polarized  (+)/(-­‐)  leads  1  μF  ~  200,000  μF  Breakdown  at  350  V

Figure  9–17            Trimmer  capacitors.

Variable  capacitor

Comments on R, L, C• Resistor: v = R x i

• For a given terminal current, the voltage drop depends on the resistance

• Inductor: v = L x (di / dt)

• For a given time-varying current, the voltage drop depends on the inductance

• Capacitance : i = C (dv / dt)

• For a given time-varying voltage, the amount of current that flows in the terminal depends on the capacitance

• In one aspect, R, L, C all do similar thing!

• They determine the current or voltage of the element

• They determine(‘resist’ or ‘impede’) the current flow for a given voltage

• A strict concept of impedance will be introduced later in this course