ENTC 4350BIOMEDICAL

INSTRUMENTATION I

POWER DISTRIBUTION

The power company, in providing electricity to the home, hospital, or laboratory, uses alternating current (AC) instead of direct current (DC) because of the ease with which AC can be transformed from one voltage to another, • For example, from the high voltage of the

transmission lines to the 115 volts of the home.

This is done with a device called a transformer.• Note that the power company uses high

voltages at low currents for the long-distance transmission of electricity in order to hold down IR losses.

• Whereas lower voltages—115 or sometimes 230 volts—are used for safety reasons in places where people live and work.

At this point, you are probably dying with curiosity to know what the differences are between AC and DC power.

The following voltage-versus-time signals in are all considered DC or direct current, because the voltage does not cross the zero axis.

In general, all signals that do not cross the zero axis are considered DC, • even though they might vary somewhat with

time.

• Where we have a regularly varying AC voltage superimposed on a DC voltage, we will call it DC with an AC component.

In an AC or alternating current signal, the voltage is first positive and then negative. • For every positive peak, there is a negative

one of the same size and shape. • It is the type of signal that is most conveniently

transformed to higher or lower voltages.

Voltage Indicators

Vrms = Vp · .707 (Sine wave)

VppVrms Vp

For AC waveforms, we speak of its frequency, f. • This frequency is just the number of cycles

the voltage makes each second; • Each cycle is composed of one complete positive

peak and one complete negative one, • That is, the voltage must go up, come down, and

come back up to zero again to complete one cycle.

f = 1/T = 2f

Frequency and PeriodPeriod, T

f1( )t

The unit most commonly used for frequency is the hertz (Hz).• Named after Heinrich Rudolph Hertz, a 19th

century German physicist.

• One hertz is simply one cycle per second, • 60 Hz is 60 cycles per second.

We will spare you any funny stories about how EEs came to call cycles per second “hertz,” because it only hertz when we laugh.

There might be lots of other AC frequencies about, but 60 Hz is what is used for power in the United States, and thus it is the most common frequency. • It takes exactly 1/60 of a second for one

complete cycle, which is the same as saying that there are 60 cycles per second.

An apparent problem arises in talking about AC. • Namely, what voltage value should we use?

• It is positive at one time, negative at another time, and zero in between. • This was a real hassle for Thomas Edison, and he

never quite got used to the idea of AC power.

We now have a simple answer to this problem, though the mathematics by which it was obtained are complex.

We begin by noting that it would be convenient to have our equations such as W = I2R and I = VR yield the same results with either DC or AC. • With DC, there is no question about what values to

use for V or I, because when they are given, they are either constant or vary so slowly that they may be assumed constant.

• With AC, however, this is not the case, and after some mathematical manipulations, it was decided that the so-called root-mean-square or RMS values would be used.

The RMS value is obtained by multiplying the peak value of the voltage or current by 0.707. • If the peak voltage is 163 volts, for example,

the RMS value is 115 volts

The next question may be, how does the use of RMS values make our electrical equations come out all right? • This RMS business may seem like some kind

of a trick, and it is, but it makes our equations work.

Consider two 40-watt light bulbs, one operating on AC and the other on DC. • The brightness B of each bulb is a function of

the current: B = kI2,• where k is a constant.

When the bulbs are equally bright, we can assume that the AC and the DC currents are equal.

The power output of the DC bulb is: • W = IV.

• If W = 40 watts and V = 115 volts, I must he 0.348 amp.

If this is the current through the DC bulb, what is the current through the AC bulb?

Since the bulbs are equal in brightness, they must have equal effective currents. • It follows that I(DC) must equal I(AC).

In this case, the value of I(AC) is 0.348 amp RMS. • The peak value of the current is about 0.5 amp, but

this is academic.

• The RMS value of 0.348 amp works in our equation because 0.348 amp times 115 volts (RMS) equals 40 watts (of any kind).

• The peak values of 0.5 amp and 163 volts will not work, because the product of these would give about 82 watts, but the bulb in fact would burn no brighter.

Wattage or power is the same, then. whether AC or DC is used, so long as the RMS values of the AC voltages or currents are used in its computation. • Note, too, that the concept of resistance,

when applied to resistors, stays the same in either AC or DC. • The point is that the AC resistance of a resistor is

the same as its DC resistance. and there is no such thing as RRMS.

* RMS is a measure of a signal's average power. Instantaneous power delivered to aresistor is: P= [v(t)] /R. To get average power, integrate and divide by the period:

RMS: Root-Mean-Square

2

Pavg= 1 1 [v (t)]dt = (Vrms)

R T R

t0

t0+T 2 2

Solving for Vrms: Vrms= 1 [v (t)]dt

T

t0

t0+T 2

* An AC voltage with a given RMS value has the same heating (power) effect as a DC voltage with that same value.

* All the following voltage waveforms have the same RMS value, and should indicate1.000 VAC on an rms meter:

1.414 v1.733 v

1 v 1 v

WaveformVpeakVrms

Sine1.4141

Triangle1.7331

DC11

Square11

1

All = 1 WATT

ENTC 4350

POWER DISTRIBUTION

The Generator or Electricity Pump

The power plant has a big coil of wire built into a complex device called a generator. • When the coil is rotated through a magnetic field, the

electrons in the coil move in response to the magnetic force.

• We could say that the “electron pressure is increased at one end of the wire and reduced at the other.

• If the coil is attached through wires to a light bulb. which we call a load, the current flows out of one end of the wire (the high-pressure side) and back to the low-pressure side through the load.

We may note that the same type of situation exists with the heart. • The heart does not produce blood:

• The heart just raises the pressure so that the blood can flow through the body.

Similarly, our friendly electric company does not produce electricity; • The copper wires are already full of electrons.

The power company raises the electron pressure so that the electrons will flow through the wires to the hospital to provide • power,

• heat, and

• light.

Moving the wire through the magnetic field raises the electrical pressure (voltage) at one end of the wire and reduces it at the other. • Notice that all the electricity always

comes back to the generator. • The power company sells it at high

pressure and gets it back at low pressure.

• All the coal, oil, or water power they use is needed just to push the coil through the magnetic field.

The power company uses not one, but three wires or coils that follow each other through the magnetic field. • At any given instant, when one coil is at high

pressure, the other two coils will be at a lower pressure.

• At every instant of time, then, there will be at least two coils that are not at zero voltage.

The output from all three coils is carried through the city as three phase power.

Ground and Neutral The generator has three output wires

(one from each coil) plus a fourth wire called ground.

Ground is exactly that. • It is a big, copper plate buried in the earth at

the power plant. • One end of each of the three coils is connected to

the copper plate.

• This will insure that all the electricity that the power company sends out comes back home again.

The points to remember are • First, the power company distributes

electricity by means of this system of three hot wires plus one ground wire, and

• Second, each of the three hot wires can deliver power directly to a load.

Most homes or hospitals use, the three-wire system converted into the more familiar hot, neutral, and ground configuration.

The ground wire is an important part of the hospital safety program. • It is the return pathway for any electricity that

might leak out in a defective appliance.

You may be curious as to how the three hot wires and one ground wire turn into the one hot, one neutral, and one ground wire. • But simply note that

• the neutral is the normal path by which electricity moves back toward the power plant, and

• the hot and ground wires are effectively the same as shown before.

We note that eventually all four wires arrive at the hospital via power poles or underground cables.

On the power poles, the ground wire is carried at the top of the pole in the hope that if lightning strikes, it will hit the ground wire and go into the earth.

Power is moved across country through transmission lines at a higher voltage than that used in the home or hospital, which is done to save money. • Delivering electricity at high pressure is

economical because the loss in the wires is reduced.• Nature discovered the idea and used it first.

The advantage of a high P and a low Q lies in the fact that the pressure drop P = QR. • Thus, for a given resistance R, we can reduce

the pressure drop by using a small value of Q.

• This effect appears again in the heat production equation, W = Q2R.• Once again, for a given R, we can hold down the

value of W by going to a smaller value of Q.

Nature has taken advantage of the previous relationship by making the arteries of a strong, tough material that can withstand high pressures. • Because the blood flow in the arteries is quite

fast, only a limited number of arteries

In the vascular system, the number of veins is far greater than the number of arteries, and the venous area is greater than the arterial area.

This makes sense if we note that the power output of the heart is given by the equation • Wo = PQ.

• This means that we can reduce the flow Q as long as we increase the pressure P to keep the product PQ the same. Q. are needed.

With the veins, however, it is another story. • The pressure is low and the flow is slow, and

• a large venous area is required.

• The veins do not have to be as strong as the arteries, • which is why nurses prefer to “stick” a vein instead

of an artery.

The power company, then, transmits power between cities at high voltage (300,000 volts) to save money on copper wire.

At the hospital, these voltages are reduced to 230 and 115 volts for safer application.

Electricity comes in through the panel board (which is usually in the utility closet), then it goes through fuses or circuit breakers, and it finally passes through wires behind the walls or ceilings to the receptacles.

The receptacles are where you actually plug in to get the electricity. • Notice that the power comes in through the hot lead

and goes back to the power company via the neutral lead. • Of course, the electricity only flows if something is

plugged in and turned on.

It may help if you think of the hot wires as arteries and the neutral wires as the veins.

Blood flows from the heart to the arteries and returns to the heart via the veins. • The situation with electricity is much the

same, only the names are different.

A three-wire, female receptacle is depicted, into which we are going to plug a two-wire appliance (a heater).

We can think of the electricity as flowing out of the hot side of the receptacle, through the appliance, and back to the power plant via the neutral lead. • If there are one or more appliances connected

to the various outlets, there will be a significant current flow in the neutral wire.

This in turn means that a voltage must exist; • no flow occurs without a pressure to push it along.

From this, we may conclude that the neutral wire is not the same as ground, electrically speaking. • Neutral is the line through which the low-pressure

electricity flows back to the power plant.

• The ground wire is at the potential of the earth.

In modern buildings, you will find three-wire or grounded outlets.• The openings are

arranged as shown.

• Note the unusual shape of the ground connections

• This enables us to identify the ground connection.

The ground wire is what makes the difference between shock or no shock if the appliance is defective. • If all home or hospital appliances were guaranteed to be

always perfect, no ground wire would be needed.

The defective heater has been plugged into a grounded receptacle and a person has one hand on the heater and the other on a metal sink.

The sink is connected to earth ground by means of the water pipes.

What happens to the person?

Nothing! • Some of the electricity flows out of the hot

side of the receptacle, through the appliance, and back to the power plant via the neutral wire, but the electricity that leaks off into the defective appliance goes back through the ground wire. • The nurse is quite safe, but if there were no

ground wire, the result might have been much different.

The electricity that leaked out through the defect follows the path of least resistance to whatever ground it could find.• Without an instrument ground, the person with

a hand on the well-grounded sink might experience the shocking revelation that she was part of the path—provided she lived to realize that fact.