BME50 Lecture 4 This material is intended for use by Tufts University students for educational purposes.
Modeling the human body
Electrical Aspects
BME50 Lecture 4 This material is intended for use by Tufts University students for educational purposes.
Brief electronics refresher
Current (amount of charge that passes
through a given point in a specified time
period.
Define the direction/sign for the current
current is positive if:
-positive charge is moving in the
direction of the arrow
-negative charge is moving in the
direction opposite to the arrow.
Kirchoff's current law:
Current can flow in a closed circuit (No current is lost as it
flows around a circuit / net change cannot accumulate
within a circuit element charge must be conserved).
Whatever current enters one terminal
must leave the other
At the nodes (defined as the place where
two or more circuit elements have a
common connection) the sum of the
current must be zero
i ii(t) = 0
Definitions:
Node: a point at which two or more circuit elements have
a common connection
Branch: A circuit element/ connected group of circuit
elements
Path: A connected group of circuit elements in which
none is repeated
Closed path: A path that starts and ends at the same
node.
Mesh: A closed path that does not contain any other
closed paths within it
Essential node: A point at which three or more circuit
elements have a common connection
Essential branch: A branch connecting two essential
nodes
Voltage
Voltage represents the work per unit
charge associated with moving a charge
between two points
Technical definition: the line integral
of the electric field E.
V is a constant (DC) source
v is a time-dependent source
Nerve cell action potential: 40-110 millivolts
Single-cell battery: 1.5 volts
Automobile electrical system: 12 volts
Household mains electricity: 120 volts North America, 230 volts Europe
High voltage electric power transmission lines: 110 kilovolts and up
Lightning: 100 megavolts
Kirchoff's Voltage law
Analogous to Kirchoff's current law it tells us that
i vi(t) = 0
or that the sum of all voltage drops (conventions = the sign of a voltage drop
around a closed path is zero. is the first sign encountered while moving
across the path)
POWER/ ENERGY
The power P is measured in Watts
w is the energy measured in Joules
Convention dictates that if power is positive, it's being delivered or
consumed by the circuit element.
A negative value for power indicates is being extracted (generated)
by the circuit element (i.e. a battery)
A circuit element can be either active or passive
passive elements are elements for which
the power is always >0 or zero
It can either
be dissipated as heat (resistance)
stored in an an e-field (capacitor)
stored in a magnetic field (inductor)
active elements are capable of generating energy.
Sources
two terminal devices that + +
provide energy to a circuit.
VS - VS - IS
dependent sources +
(where the voltage or current -
is a function of some other
voltage or current in the
circuit).
Resistance
Resistors
(circuit element that limits the flow of
current)
measured in ohms ()
The power consumed by a resistor is
Capacitors
passive element that stores energy in an
electric field by charge separation when
appropriately polarized by voltage
plates separated by a gap (filled with dielectric).
they contain a bunch of electric dipoles
that become polarized in the presence of an
electric field.
the charge separation is proportional to the external voltage
The temporal relationship (i-v) is written in
a more useful form as
Dielectric breakdown occurs when a charge buildup exceeds the electrical limit or
dielectric strength of a material. The negatively charged electrons are pulled in one
direction and the positively charged ions in the other. When electrons are removed
from a nucleus, it becomes positively charged. When air molecules become ionized
in a very high electric field, the air changes from an insulator to a conductor. Sparks
occur because of the recombination of electrons and ions. Lightning occurs when
there is a buildup of charge on the clouds and the ground It produces the electric
field that exceeds the dielectric strength of air. Ionized air is a good conductor and
provides a path where by charges can flow from clouds to ground.
The dielectric strength of air is approximately 3 kV/mm. Its exact value varies with
the shape and size of the electrodes and increases with the pressure of the air.
3 x 106 V/m
The Physics Factbook
Edited by Glenn Elert -- Written by his students
An educational, Fair Use website
Inductors
It's a passive element that is able to store
energy in a magnetic field (a magnetic
field is established when the current flows
through the coil).
Resistors in series
V +
-
Resistors in parallel
+
-
Voltage Divider Rules
V +
-
Current Divider Rules
+
-
Electrical safety
of paramount importance!
If sufficient current is allowed to flow through the
body, significant damage can occur
Dangers of Electrical Shock
The severity of injury from electrical shock depends on the amount of electrical current and the length of
time the current passes through the body. For example, 1/10 of an ampere (amp) of electricity going
through the body for just 2 seconds is enough to cause death. The amount of internal current a person can
withstand and still be able to control the muscles of the arm and hand can be less than 10 milliamperes
(milliamps or mA). Currents above 10 mA can paralyze or "freeze" muscles. When this "freezing" happens,
a person is no longer able to release a tool, wire, or other object. In fact, the electrified object may be held
even more tightly, resulting in longer exposure to the shocking current. For this reason, hand-held tools
that give a shock can be very dangerous. If you can't let go of the tool, current continues through your
body for a longer time, which can lead to respiratory paralysis (the muscles that control breathing cannot
move). You stop breathing for a period of time. People have stopped breathing when shocked with
currents from voltages as low as 49 volts. Usually, it takes about 30 mA of current to cause respiratory
paralysis.
Currents greater than 75 mA may cause ventricular fibrillation (very rapid, ineffective heartbeat). This
condition will cause death within a few minutes unless a special device called a defibrillator is used to save
the victim. Heart paralysis occurs at 4 amps, which means the heart does not pump at all. Tissue is burned
with currents greater than 5 amps. 2
http://www.cdc.gov/NIOSH/docs/2002-123/2002-123b.html
Electrical safety
A current of 50 mA
is enough to cause
ventricular fibrillation
I=15mA if you
hold a car battery by its leads
Electrical safety shocks of the right kind
Defibrillation results in the generation of an electrical potential difference across
the heart and the passage of current. The passage of an electrical shock of the
order of 100 mA/cm2 through the ventricles for 2 to 20 msec will simultaneously
stimulate most ventricular muscle cells resulting in the potentially excitable cells
to enter a state of refractoriness. This sudden change in state of myocyte
excitability results in the block of the multiple waves of excitation that constitute
fibrillation Babbs CF 1994.
Design of biologically relevant electronic
instrumentation
from here we
can go one of two
ways
Use these element / interconnection rules
to model biological systems
Design of biologically relevant electronic
instrumentation
http://instruct1.cit.cornell.edu/courses/eceprojectsland/STUDENTPROJ/2003to2004/jms225mm246/ElectrocardiogramSystem.pdf
Design of biologically relevant electronic
instrumentation
http://www.analog.com/library/analogDialogue/archives/29-3/low_power.html
