ECE 252 Introduction to Electrical Engineering

Lesson 18. Batteries, Voltage Regulators, Transformers, and Sensors


Batteries are everywhere.  They're in cell phones, cameras, cars, and computers.  Some are primary batteries (non-rechargeable) and some are secondary batteries (also called rechargeable or storage).  Engineers need to know the properties of batteries so that they can design batteries into equipment and so that they can analyze equipment that uses batteries.  A Power Point slide show on batteries can be found at BatteryBasics.pps.

Primary Batteries

Batteries for flashlights, hearing aids, and toys are frequently primary batteries.  You use the device until the batteries wear out, and then you throw the batteries away.  Typical battery sizes include D, C, AA, and AAA.  The most basic of these batteries use zinc-carbon technology.  They are frequently labeled as "heavy duty."  Ironically, such batteries are the poorest-performing batteries.  Zinc-alkaline batteries (frequently just called "alkaline" batteries), although somewhat more expensive, have higher energy density than the zinc-carbon batteries.  For both of these battery technologies, the voltage decreases steadily during discharge.  Although the battery may start out at slightly higher than 1.5 V, it will decrease to about 0.8 V by the end of its useful life.

Hearing aid batteries are usually zinc-air button cells.  The voltage of these batteries remains fairly constant over their lifetime.  Lithium-ion primary batteries can occasionally be found in applications such as digital cameras.

Secondary Batteries

Technologies for rechargeable batteries include sealed lead-acid (SLA), nickel-cadmium (NiCd), nickel-metal-hydride (NiMH), and lithium-ion (Li-ion).  each of these technologies has its advantages and disadvantages.  All of them have the advantage that their voltage output remains substantially constant over their useful life.  The table below lists some of the advantages, disadvantages, and features.  Although it is not a secondary battery, an alkaline battery is also listed for comparison purposes.

Technology Cost Energy
Alkaline Low High 1.5 V 150 mΩ (AA size) Not rechargeable.  Voltage decreases over life.  Long shelf life.
SLA Low Low 2 V ? The most bang for the buck, but at the expense of size and weight.  Acid is dangerous.  Lead is toxic.
NiCd Moderate High 1.2 V 30 mΩ (AA size) Suffers from "memory effect."  Cadmium is toxic.  Low shelf life.
NiMH High High 1.2 V 150 mΩ (AA size) Good choice for many rechargeable battery applications.  Low shelf life.
Li-ion Very high Very high 3.6 V 320 mΩ Best energy density.  The battery of choice for cell phones and laptops.  Dangerous if overcharged.  2-3 year lifetime.  No "memory effect."

The "energy density" is the storage capacity of the battery compared to its mass.  Lithium ion batteries have the best energy density, so it's not surprising that they are used for devices that must minimize battery weight, such as cell phones and iPods.

The "cell voltage" is the nominal voltage of one cell of the battery.  Six 2 V SLA cells are used to make a 12 V automobile battery.

NiCd and NiMH batteries are frequently used as replacements for alkaline batteries.  This may seem odd, as the alkaline battery has a significantly higher nominal voltage (1.5 V vs. 1.2 V).  Nevertheless, the rechargeable batteries usually work quite well.  The rechargeable batteries have relatively flat discharge curves, maintaining their 1.2 V nominal value over a significant period of their life span.  The alkaline battery's voltage drops off quickly with use, and is down to about 1.2 V when half its life is gone.

The capacity of a battery refers to the charge a battery can hold.  This is usually measured in ampere-hours (Ah) or milliampere hours (mAh).  For example, a typical AA NiMH battery may have a capacity of 2500 mAh.  From this example, one might think that this battery can provide 2500 mA for one hour.  This may not be the case, as it depends on the conditions under which the capacity was measured.  Rather, the battery may be able to provide 25 mA for 100 hours.  In any case, the effective cell capacity decreases as the current increases.  In a high-current application, the capacity must be derated.

The capacity is an important consideration when selecting a battery for an application.  If, for example, a cell phone design requires a battery that will allow for 6 hours of talking before recharge, the current must be determined, and then multiplied by 6 hours to get the required minimum battery capacity.

Sealed lead-acid (SLA) batteries in 12 V size are used in most automobiles.  SLAs should not be subjected to deep discharge as this shortens their service life.

The "memory effect" refers to a decrease in battery performance that depends on charging history.  If a battery is partially discharged, and then recharged, and if this discharge/recharge cycle is done repeatedly, the battery capacity will decrease.  The memory effect can be reduced by periodically completely discharging the battery before recharging.  NiCd batteries are particularly prone to the memory effect.

NiMH batteries show a slight memory effect, so they should be drained occasionally, but not often.  NiMH batteries are commonly used in hybrid vehicles such as the Prius.

Li-ion batteries have no  memory effect, and should never be subjected to a deep discharge; draining a Li-ion battery shortens its life.  Unnecessary recharging of a Li-ion battery also shortens its life.  A balance should be struck between avoiding deep discharge and recharging too soon.  Regardless of the number of charge/discharge cycles, a Li-ion battery has a short lifetime - perhaps three years.  Li-ion polymer batteries have similar properties to Li-ion batteries.  They have the advantage that they can be molded into many shapes.

Batteries are not ideal devices.  They have internal resistance.  The values given in the table above are approximate, and are for fully-charged, fresh batteries.  Note that these values are in milliohms.  The actual internal resistance will depend on the charge level and the number of recharge cycles the battery has experienced.  When drawing heavy current from a battery, the terminal voltage will be reduced because of the voltage drop across the internal resistance.

Batteries in Series and Parallel

In order to achieve a desired voltage, it is frequently necessary to connect batteries in series.  For example, if you open up a 9 V battery, you will find that it is made with six 1.5 V batteries in series.  Some guidelines are in order when selecting batteries for a series installation:  Use only batteries of the same type (e.g. all alkaline) with the same discharge history (e.g. all fresh).  One of the reasons for this caution is that, with some rechargeable batteries, polarity reversal can occur.  When a rechargeable battery is deeply discharged, its polarity may reverse, with its negative and positive terminals swapping.  The battery may be permanently damaged and may overheat.  This is usually only a problem when multiple batteries are in series.

If it is desired to increase current, rather than voltage, batteries can be connected in parallel.  This is not usually a good idea, but if it is necessary, be sure that all batteries are of the same type with identical charge histories.  The principal problem of connecting batteries in parallel is that good batteries can discharge through bad ones.  Even if all the batteries are of the same type (e.g. all NiMH), the batteries may have slightly different voltage or discharge characteristics, and current may flow among the parallel batteries.

Voltage Regulators

Many electrical devices require DC voltages.  Some need several different DC voltages.  Batteries can provide these voltages, but batteries may need frequent recharging or replacing.  Although a battery may be appropriate for a cell phone, which must be portable, it would not be appropriate for a clock radio, which is usually left in one place and has access to an electrical socket.  Instead of a battery, the clock radio would have a power supply that converts AC to DC and provides a smooth DC voltage for the clock's electronics.

One of the components of a power supply is a voltage regulator.  Its job is to convert one DC voltage level to another.  The simplest kind is a linear voltage regulator, as shown in the figure below.

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The LM 7805 above is a typical linear voltage regulator.  It can provide an output of 5 V for an input between 7 V and 35 V with a current up to 1 A (with proper heat sinking).  The two capacitors must be provided to get the voltage regulator to work properly.  The output voltage Vo can be attached to any circuit requiring 5 V, and the voltage will be stable over a wide range of currents.

A voltage regulator from the LM 78xx series can be selected to provided an output voltage of  5, 6, 8, 9, 10, 12, 15, 18, or 24 V.

A diagram of the LM7805 is shown below.

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Linear voltage regulators such as the LM7805 waste energy.  The loss will be approximately equal to (input voltage - output voltage) x (output current).  The heat generated by this loss must be dissipated. The LM7805 can only dissipate 2.5 W without a heatsink.  Nevertheless, the simplicity and versatility of this device makes it a popular choice for many applications.

The switching regulator is a greener device.  It can convert one voltage to another with very little energy loss.  An oversimplified explanation of the operation is that the device rapidly switches the input voltage on and off, with the average voltage being available at the output.  An example of a switching regulator is the DE-SW050 by Dimension Engineering (  It's a direct replacement for the LM7805, but it costs more.

Some switching voltage regulators can produce voltages greater than the supply voltage.  Some switching regulators require many additional components, frequently including inductors and zener diodes.  Most switching voltage regulators do not require heatsinks.  The power supply in your PC is a switching voltage regulator.

Before going on, you should complete Tutorial 18 on batteries and voltage regulators.


The transformer is a basic electrical device used for converting one AC voltage into another.  Its operation is based on Faraday's Law, which states that a changing magnetic flux will induce a voltage.  This is shown in the basic diagram below.

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Wire is wrapped around a core of soft iron.  When an AC voltage v1 is applied, a current i1 results.  This current causes magnetic flux to occur in the iron.  B is the magnetic flux density in webers/m2, and H is the magnetic field intensity in A/m.  The changing magnetic flux induces a voltage v2, which can produce a current i2 if there is a load connected to the output.  The soft iron core is used to contain the flux so that there is good magnetic coupling between the two coils.  The interaction between the two coils is known as mutual inductance.

If there is no loss of flux (and no other losses), then the power out is equal to the power in by conservation of energy:

v2i2 = v1i1

The circuit symbol for a transformer, along with its labels and connections, is shown below.

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The primary side is where the AC voltage is applied.  There are N1 turns of wire on the primary side.  The voltage V1 is the RMS value of the primary voltage.  I1 is the RMS value of the primary current.  The application of the primary side voltage results in the secondary side voltage (V2) and current (I2).  The secondary has N2 turns of wire and can be connected to a load Z2.  The two vertical bars between the coils of the transformer indicate that the transformer has an iron core.

For an ideal transformer (one with no losses), the following equation applies:

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N1/N2 is the turns ratio of the transformer.  By selecting the number of turns of wire on the primary and secondary of the transformer, almost any desired output voltage (V2) can be achieved.  If N2 > N1, the transformer is called a step-up transformer, because V2 > V1.  If N2 < N1, the transformer is called a step-down transformer.  Note that I2 is in the numerator of the equation.  As V2 increases I2 decreases.  This must be so to satisfy conservation of energy.  The term Z1 does not appear in the diagram for the transformer.  That is because Z1 does not represent a physical impedance; it is the apparent impedance of Z2 as seen from the primary side of the transformer.  In other words, by Ohm's law it is V1/I1.

It should be noted that transformers only work with AC.  A DC voltage applied to the primary of a transformer will result in a brief voltage pulse on the secondary.

The majority of transformers are used in power applications.  Step-up and step-down transformers are used to deliver commercial power.  Power transformers are used in electronic equipment to reduce 120 V to lower voltages that can then be rectified to produce low DC voltages.  Power transformers usually have high efficiency. Signal and audio transformers are used to couple amplifier stages.  Impedance matching transformers are sometimes used in such applications as matching speaker impedance to amplifier impedance for maximum power transfer.

Power transformers are quite efficient, perhaps 98%.  Therefore use of the ideal transformer equation is usually justified.

A power transformer nameplate will usually list primary voltage, secondary voltage, and a VA rating. The VA stands for volt-amps. it's the apparent power, a concept introduced earlier along with the power triangle. Recall that apparent power is VI, the product of rms voltage and rms current. The VA rating is the maximum apparent power that should be drawn from the transformer.

Transformer Example

A certain transformer has a 120 V primary, a 15 V secondary, and a 50 VA rating. a) If the secondary is connected to a resistance of 10 Ω, what is the current in the primary? b) What is the resistance seen on the primary side? c) What is the maximum current that should be drawn from the secondary of the transformer?

a) I2 = V2/Z2 = 15/10 = 1.5 A

I2/I1 = V1/V2

I1 = I2(V2/V1) = 1.5(15/120) = .1875 A

b) Z1 = V1/I1 = 120/.1875 = 640 Ω

Another way of calculating Z1:

V1/V2 = √(Z1/Z2)

Z1 = Z2(V1/V2)2 = 10(120/15)2 = 640 Ω

c) V2I2Max = 50 VA
I2Max = 50/15 = 3.33 A


Engineers frequently encounter many different kinds of sensors:  light, sound, temperature, pressure, strain, and more.  A sensor may respond to the stimulus by providing a change in voltage, current, resistance, or some other parameter.  The engineer must know how to apply, analyze, and (occasionally) design devices with sensors.  This task is often difficult because the sensor output may be of low intensity and may be contaminated by noise.

Wheatstone Bridge

One device that is commonly used with sensor circuits that depend on resistance is the Wheatstone bridge, shown below.

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E is the excitation voltage.  RX is the sensor.  The other resistors are included to allow the bridge to work.  When the bridge is "in balance," RX = R2, and the output voltage (Vo) is zero.  If RX increases, Vo becomes positive.  By the voltage divider equation (applied twice):

Vo = E[RX/(RX + R1) - R2/(R2 + R1)]

The relationship Between Vo and RX is not strictly linear, but for small changes in RX, Vo is approximately equal to KRX, where K is a constant depending on R1 and R2.  The important thing is that the output voltage will depend on RX, and therefore the output can be calibrated to measure the sensing parameter that changes RX.

Thevenin Equivalent of a Sensor

A sensor can frequently be characterized by its Thevenin equivalent circuit, as shown below.

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For simplicity, we will assume that the impedance can be approximated by its resistance.

The sensor is often connected to an amplifier to increase the sensor's voltage to a usable level, as shown below.

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The amplifier will have some input impedance (simplified as a resistance).  For maximum power transfer, we might want to set Rin equal to RT.  Often, this is neither possible nor desirable.  It may not be possible because the Thevenin resistance of a commercial sensor may not match well with the input of a commercial amplifier.  It may not be desirable because current in the sensor might distort the sensed parameter.  Therefore, most instrumentation amplifiers are made to have a relatively high input impedance.  If the input impedance of the amplifier is significantly greater than RT, then the input voltage (Vin) will be nearly equal to the Thevenin voltage of the sensor (VT).

Sensors as Current Sources

Some sensors behave more like current sources than voltage sources, for example photodiodes, where the current is proportional to the light intensity.  In such cases, a low input impedance is desired.  A circuit that is frequently used in such applications is the current-to-voltage converter, sometimes called a transimpedance amplifier, as shown below.

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This circuit will require some explanation.  At first glance, it appears that the photodiode is installed backwards.  This is not the case.  The photodiode conducts current in the reverse direction proportional to the intensity of the light that is falling on it.  The battery VB is present to provide the reverse bias necessary for the photodiode to operate.  In some cases, the bias battery can be left out.

The op-amp on the right takes care of converting the photodiode current (IS) into a voltage.  We will treat the op-amp as ideal.  Note that the positive input of the op-amp is grounded.  Therefore, the negative input is at ground potential (zero volts).  The op-amp looks like zero resistance from the point of view of the photodiode; this is necessary to allow the photodiode current to be truly proportional to the light intensity.  IF is the feedback current equal to Vo/RF.  Kirchhoff's Current Law can be applied to the negative terminal of the op-amp:

-IS - Vo/RF = 0

Vo = -ISRF

The output voltage is therefore proportional to the photodiode current.  The output is reversed in sign, but this should not cause any difficulty.


The resistance of a thermistor is proportional to temperature, according to the equation,


To make use of this property, it is necessary to convert the change in resistance to a change in voltage.  The circuit shown below performs this function.

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Errors in Measurement Systems

All measurement systems suffer from bias errors, which are also known as systematic errors.  Some of these errors are:

When employing a sensor, one should be aware of what types of errors to expect.  Some of the errors can be corrected by appropriate manipulation of the results.  For example, with random errors it is often appropriate to make many measurements and then take an average of the results.

Noise Minimization in Sensor Systems

Signals from sensors are typically small, perhaps microvolts to millivolts.  As such, they frequently need to be amplified.  Unfortunately, any noise that is present at an amplifier's input can be amplified along with the desired signal.

One way to do the amplification is to use a single-ended amplifier, as shown below.

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This is the easiest, but perhaps the poorest amplifier configuration.  Noise introduced on v2 will be grounded, but noise introduced on v1 will be amplified along with the signal.

For noise cancellation, a differential amplifier, also known as a difference amplifier, is often preferred, as shown below.

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Notice that the neither of the sensor leads is grounded.  It is likely that the noise on v2 will be almost the same as the noise on v1.  Therefore these two noise signals will cancel each other out and will not be amplified along with the signal from the sensor.  When selecting a differential amplifier for applications such as this, pick one with a high CMRR (common-mode rejection ratio).  That's a measure of how good the amplifier is a cancelling out signals that are the same on both input terminals.

One of the ways noise can be generated in sensor systems is by ground loops.  When a system is grounded in more than one place, small currents can flow in the ground paths.  This is because the two grounds may have slightly different potentials.  If these currents flow in a cable connecting a sensor to an amplifier, a noise voltage can be created.  To avoid this problem, one should make sure that a system is grounded in only one place.

A cable between a sensor and an amplifier acts like an antenna.  It can pick up electromagnetic radiation and convert it to a noise voltage.  There are several cabling approaches to reducing the effect of this noise, listed in order of increasing effectiveness:

Coaxial Cable.  This type of cable, frequently called coax has a central conductor surrounded by a flexible metal shield.  One of the sensor outputs is connected to the central conductor, and the other is connected to the shield, as shown below.

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The shield is grounded.  Noise impinging on the shield will be shorted to ground.  The central conductor is shielded from the noise.  This configuration cannot be used with a differential amplifier because one of the conductors is grounded.

Twisted Pair.  This configuration uses two unshielded conductors twisted together, as shown below.

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The noise impinging on the two conductors will be very nearly the same.  This configuration works well with differential amplifiers.

Shielded Cable.  In this configuration, the two conductors are encased within a shield, as shown below.

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The grounded shield protects the conductors from noise.  This configuration can be used with a single-ended or (better) a differential amplifier.

Shielded Twisted Pair.  This configuration combines the noise shielding characteristics of shielded cable with the noise cancellation characteristics of twisted pair.  It is shown below.

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This configuration can be used with a single-ended or differential amplifier.

At this time you should complete Tutorial 18A on transformers and sensors.