Bichop R.H. (Ed.) Mechatronic Systems, Sensors, and Actuators: Fundamentals and Modeling

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21-22 Mechatronic Systems, Sensors, and Actuators

In summary, when the transistor is saturated, it acts as a closed switch. When a transistor is in the cutoff

region, it acts as an open switch. When it is in the active region, it acts as a current (i

) controlled current

) amplifier. Although this is a very simplistic approximation, it is very useful for designing and

understanding power electronics and interfacing electromechanical systems. Figure 21.35 illustrates some

examples of BJT devices and applications.

When carefully controlling the base-emitter voltage

and base current

, the transistor can be made

to operate between the cutoff and the saturation region, which act as a switch, see Figure 21.36. Realistically,

transistor switching is not instantaneous (see Figure 21.37). The turn-on time

of the transistor is the

FIGURE 21.35 Some examples of using BJT.

FIGURE 21.36 BJT as a current controlled switch.

FIGURE 21.37 BJT switching characteristics.

Photo-intrerrupter

Opto-isolator

LED

–

OUT

Using BJT as a switch to turn

off/off a LED

–

OUT

CE(SAT)

Cutoff

Saturation

∪

OUT

––

OFFOFF

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Actuators 21-23

sum of the delay time

and the rise time

. Similarly, the turn-off time

OFF

is the sum of the storage

time

and the fall time

. The turn-on and turn-off time of a transistor limits the maximum switching

frequency. Typical switching frequency for a power BJT is between 2 and 20 kHz. Generally speaking, BJTs

can switch at a higher frequency than thyristors but can handle less power. Power BJTs can handle currents

up to several hundred amperes and

up to about 1 kV.

Power dissipation is a key design constraint for BJTs. Recall that if the BJT is used in the active linear

region (linear amplifier), the power dissipation is P

BJT

= i

· V

with V

> V

. With a large collector

current and considering the small volume and thermal mass of the device, the transistor is not very efficient

when operating in the active linear region. On the other hand, when the BJT is switching between saturation

and cutoff, the collector current will be small (during cutoff) and V

will be small (during saturation).

The switching power dissipation is much smaller compared with the active linear mode of operation. This

makes switching much more efficient.

One design consideration working with BJT is to supply adequate base current, especially when the

transistor is to operate in the saturated region, see Equation 21.13. This may require large input power

and may overload the input stage. As will be discussed later, this is also the main reason that BJTs are less

used in switching power electronics and are being replaced by devices such as MOSFET and IGBT, which

require much less control current. One solution to this constraint is to increase the current gain

. A

simple and elegant implementation to increase the effective current gain of a BJT is the Darlington pair

configuration.

Darlington Transistor Pairs

A Darlington transistor pair connects two BJT transistors to form an effective three terminal device that

has increased current gain, see Figure 21.38. In Figure 21.38, let

and

be the current gains of the

two transistors, then the relationship between the base current of transistor Q1 and the collector current

of transistor Q2 is

Therefore, the effective current gain for the Darlington transistor pair is the product of the two

individual current gains, i.e.,

. For a typical Darlington pair, this can be in the range of

500–10,000. The trade-off for using Darlington pair configuration is the additional space (real estate)

needed for two transistors instead of one.

Metal-Oxide-Semiconductor Field Effect Transistor (MOSFET)

MOSFET is a type of field effect transistor (FET). FETs are voltage controlled three terminal devices respec-

tively called drain (D), source (S), and gate (G). The terms come from the analogy of overhead tank system

that uses a gate valve to control the water flow from source to drain. MOSFET uses a metal plate as the gate

terminal and it is insulated from the p- or n-type silicon substrate by a thin layer of oxide (see Figure 21.39).

When a gate voltage V

is applied to the gate plate, an electrostatic field induces reverse charges at the

gate and the substrate. The charges at the substrate initiate transistor type characteristics by forming either

an n-type channel or a p-type channel. Hence, the n- or p-type MOSFET classifications (see Figure 21.39).

FIGURE 21.38 Two type of Darlington transistor pairs.

⋅

⋅()⋅

⋅()i

⋅

⋅== = =

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21-24 Mechatronic Systems, Sensors, and Actuators

For a majority of the power amplification and modulation applications, MOSFETs are designed to operate in

the enhancement mode. Figure 21.40 illustrates the enhancement mode characteristic of an n-channel MOSFET:

1. Cutoff—When the potential across the gate and the substrate (source) V

is less that the turn-on

(threshold) voltage V

, the MOSFET is in the cutoff region and there is negligible current flow

through the drain (D) terminal, i.e.,

Typically, V

≈ 1–2 V. In this mode, the transistor from D to S can be viewed as an open connection.

2. Active Region—When the V

> V

, the MOSFET is in the active region, where

In this mode, the transistor can be viewed as a voltage-controlled current amplifier, where the

drain current i

is proportional to square of the difference between the gate-source voltage and

the threshold voltage. The drain current is controlled by the gate-source voltage V

. The power

dissipation across the transistor P

FET

= i

· V

3. Ohmic State—When V

is large enough so that the drain current is determined by the drain

source circuit, the MOSFET is in saturation and

>> (21.14)

FIGURE 21.39 Metal-oxide-semiconductor (MOS) field effect transistor (FET).

FIGURE 21.40 Enhancement mode MOSFET characteristic.

Gate

p-channel MOSFETn-channel MOSFET

Source

Drain

Ohmic state

constant current

Cutoff (V

< V

)

Breakdown

(mA)

–

0≈

≈

> and

–()

∝

–>

and

()V

–<⋅≈

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Actuators 21-25

In this mode, the transistor can be viewed as a closed switch between the terminals D and S with

a voltage controlled resistance R

. The drain current i

is controlled (determined) by the drain

circuit. At rate current, the V

drop during saturation ranges from 2 to 5 V.

When operating in the enhancement mode, a MOSFET behaves very similar to a BJT. Instead of base

current, the MOSFET behavior is determined by the gate voltage. When carefully controlling the gate

voltage of a MOSFET, the transistor can be made to operate as a voltage controlled switch (Figure 21.41)

that operates between the cutoff (point A) and the Ohmic (point B) region.

One advantage of a MOSFET device is that the MOSFET has significantly larger input impedance as

compared to BJT. This simplifies the circuit that is needed to drive the MOSFET since the magnitude of

the gate current is not a factor. This also implies that a MOSFET is much more efficient than BJTs as

well as it can be switching at a much higher frequency. Typical MOSFET switching frequency is between

20 and 200 kHz, which is an order of magnitude higher than BJTs. Power MOSFETs can carry drain

currents up to several hundreds of amperes and V

up to around 500 V.

Field effect is one of the key reasons why MOSFET has better switching performance than BJT.

However, static field is also one of its main failure modes. MOSFETs are very sensitive to static voltage.

Since the oxide insulating the gate and the substrate is only a thin film (in the order of a fraction to a

few micrometer), high static voltage can easily break down the oxide insulation. A typical gate breakdown

voltage is about 50 V. Therefore, static electricity control or insulation is very important when handling

MOSFET devices.

Comparing BJT with MOSFET, we can conclude the following:

•

Both can be used as current amplifiers.

•

BJT is a current-controlled amplifier where the collector current i

is proportional to the base

current i

•

MOSFET is a voltage-controlled amplifier where the drain current i

is proportional to the

square of the gate voltage V

•

Both can be used as three terminal switches or voltage inverters.

•

BJT: switching circuit give rise to TTL logics.

•

MOSFET: switching circuit give rise to CMOS logics.

•

BJT usually has larger current capacity than similar sized MOSFET.

•

MOSFET has much higher input impedance than BJT and is normally off, which translates to less

operating power.

•

MOSFETs are more easily fabricated into integrated circuit.

•

MOSFETs are less prone to go into thermal runaway.

•

MOSFETs are susceptible to static voltage (exceed gate breakdown voltage ∼50 V).

•

BJT has been replaced by MOSFET in low-voltage (<500 V) applications and is being replaced by

IGBT in applications at voltages above 500 V.

FIGURE 21.41 MOSFET as a voltage controlled switch.

OUT

–

Ohmic region

Cuttoff

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21-26 Mechatronic Systems, Sensors, and Actuators

Insulated Gate Bipolar Transistor (IGBT)

IGBT is a voltage-controlled transistor that has the terminals identified in the same way as BJTs. IGBT

is a four-layer device that has the similar construction of a MOSFET with an additional p layer.

Figure 21.42 shows the schematic symbol and equivalent circuit for an IGBT. IGBT has the combined

characteristics of the BJT and MOSFET. Similar to MOSFET, it has high input impedance and high

switching frequency. It also has high power handling capacity like the BJT.

21.1.3.5 Typical Power Amplifiers for Electromechanical Actuators

Power amplification and modulation for electromechanical actuators are classified into two basic cate-

gories, based on the methods the respective power electronics are driven. Linear amplifiers drive the BJTs

in their active linear region. Switching amplifiers drive the transistors in on-off switch mode. Depending

on the control objective, the command signal (Figure 21.2) to the amplifier can be either a voltage or

current command that intends to modulate the electric energy delivered to the energy conversion device.

Since most of the electromechanical actuator involves driving an inductance load such as a coil winding

of an electromagnet or the rotor of a DC motor, in the following discussion, we will use the DC motor

as an example of an inductance load for the power amplifier.

Linear Amplifiers

Figure 21.43 shows the basic drive circuit for linear voltage and current control amplifiers. Both schemes

have the following commonalities:

1. The input command voltage V

(t) is applied to the base of the transistor.

2. The electric power needed to driver the load is provided by a DC supply.

3. The transistors are driven in the active linear region.

Voltage Control (Mode) Amplifier

In Figure 21.43a, the motor is driven as a load of an emitter circuit. If the base-emitter voltage is ignored,

the voltage across the motor V

is directly controlled by the input voltage V

and the current is supplied

by the power supply. The amount of current, on the other hand, depends on the applied voltage, speed,

and the motor parameter.

FIGURE 21.42 Insulated gate bipolar transistor (IGBT).

FIGURE 21.43 Two basic linear motor amplifiers.

Equivalent circuitSchematic symbol

∼V

(b) Current-mode driver(a) Volta

e-mode driver

∼

–

–V

_______

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Actuators 21-27

To provide adjustable voltage gain, Figure 21.44 shows a variable gain voltage-mode amplifier, where

the apparent amplifier gain from the command input V

to the applied motor (winding) voltage V

can be approximated by (R

+ R

)/R

, which can be adjusted by proper selection of the resistors R

and

. If a large motor current is required, transistor Q2 can be replaced by a Darlington transistor pair.

The amplifiers shown in Figures 21.43 and 21.44 can only drive the current through the motor (load)

in one direction. Hence, they are also called unipolar amplifiers. To provide bidirectional current flow,

two transistors can be connected with the motor in a push-pull type configuration, as shown in

Figure 21.45. The two diodes in the circuit are used to eliminate the dead-zone created by the base-

emitter voltage drop for the transistors. Notice that a bipolar voltage source is needed for this configu-

ration. Figure 21.46 shows a bipolar voltage-mode driver with variable gain (R

+ R

)/R

. Similarly, if

larger motor current is required, transistors Q3 and Q4 can be replaced by Darlington transistor pairs.

FIGURE 21.44 Variable gain voltage-mode amplifier.

FIGURE 21.45 Bipolar voltage-mode amplifier.

FIGURE 21.46 Bipolar variable gain voltage-mode amplifier.

≈

+ R

With diode

Push

Pull

Approximately 0.6 V

dead-zone

–V

≈

+ R

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21-28 Mechatronic Systems, Sensors, and Actuators

Current Control (Mode) Amplifier

As previously discussed, in many electromagnetic actuators, the output force or torque of the device has

strong correlation with the winding current, e.g., for a permanent magnet DC motor and a voice coil

actuator, the output torque and force are proportional to the input current. Therefore, in many motion

control applications, it is more desirable to have a voltage-to-current conversion (current-mode amplifier)

at the power stage, where the input voltage command is proportional to the current flowing into/out of

the motor (winding). Figure 21.43b shows a basic circuit for a current-mode amplifier. The relationship

between the emitter (motor) current i

and the input voltage command V

If the base-emitter voltage is ignored, the voltage across the motor current i

is proportional to the

input voltage V

, i.e., i

≈ (1/R

) · V

Figure 21.47 shows a basic bipolar current-mode amplifier. An Op-Amp is used to close the current

loop. The resistor R

, often called the sensing resistor, is used to sense the motor current for feedback to

the Op-Amp. Depending on the desired current magnitude, the sensing resistor needs to have adequate

power rating to dissipate the heat ( ) generated by flowing current through the resistor. For a zeroth

order approximation, at steady state, the Op-Amp will try to equalize the potential at the positive and

the negative terminals, i.e., it will try to make

which implies

Although a current amplifier tends to have a linear relationship between the command input and the

winding current, there is practical limitation due to the limited source voltage. In Figure 21.47, the supply

voltage is ±V. Assuming that the motor winding has resistance R

, the maximum current i

MAX

the voltage

source can supply is upper bounded by

FIGURE 21.47 Bipolar variable gain current-mode amplifier.

–V

–

----------------------

⋅

−

-----

⋅≈

−

⋅

---------------

⋅≈

MAX

-------------------

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Actuators 21-29

The above bound has not considered the effect of the back-emf that will be induced in the winding

if the winding is moving. Hence, the amount of current available for a current-mode amplifier is limited

and needs to be considered when working with a current-mode amplifier.

Switching Amplifiers

Linear amplifiers are simple and do not generate electrical noises. However, since the final stage transistors

are operating in the active linear region, significant power is dissipated into heat; this reduces the efficiency

of the device as well as requires large heat sinks to protect the components. However, as shown in

Figure 21.48, when operating in the saturation region, if the collector-emitter voltage drop is in the order

of 1 V or less, the power loss across the transistor is significantly less, given the same amount of current

flow. The trade-off is that additional circuits are needed to provide the modulation for current or voltage

control.

Figure 21.49 shows a simple switching amplifier that is simply a transistor connecting a load. It is

essentially the same as the basic linear amplifier shown in Figure 21.43a. The difference is in the way the

transistor is controlled. For a switching amplifier, the input (base) voltage only takes on two values (states),

high and low. When the base (input) voltage is high, the transistor is turned on in the saturation mode

and current will flow through the load. If we neglect the collector-emitter voltage drop, the voltage across

the load is approximately the supply voltage. When the base voltage is low, the transistor is turned off

in the cutoff state and no voltage is applied to the load. If the load has a low pass characteristic, the

average current/voltage across the load will be proportional to the turn-on time. Therefore, if the switching

frequency is sufficiently high (relative to the load impedance), the effective voltage/current across the

load can be modulated by the percent high input voltage, e.g., if the V

is high 80% of the time, the

average voltage across the load will be close to 80% of the supplied voltage V. This is the so-called pulse-

width modulation (PWM). Another benefit of using switching amplifiers is that V

can be directly interfaced

with a digital device without the need for a DAC.

Push-Pull (Class B) Power Amplifier

The switching amplifier shown in Figure 21.49 is unipolar, i.e., it can only drive current through the load

in one direction. Figure 21.52 shows a simple

push-pull

(

Class B

) type power stage to supply bi-directional

current to the load. The circuit in Figure 21.50 is very similar to the bipolar voltage-mode amplifier shown

FIGURE 21.48 Power dissipation in transistors.

FIGURE 21.49 Simple switching amplifier with switching input.

Operating point

Power dissipated

in the transistor

(b) Transistor in saturation region

(a) Transistor in active linear re

ion

Power dissipated

in the transistor

load

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21-30 Mechatronic Systems, Sensors, and Actuators

in Figure 21.45. The difference is also in the way the transistors are controlled. When the base voltage

is sufficiently positive (

), the push transistor Q

push

will be turned on and the pull transistor Q

pull

will

be turned off. This results in a load current flowing from positive supply to ground. If the base voltage is

sufficiently negative (

−

), Q

push

will be turned off and Q

pull

will be turned on, which results in a current

flow from ground to the negative supply. To modulate the load voltage/current, PWM can also be used.

This configuration is also called a

half H-bridge

driver or half-bridge driver for short. From an implemen-

tation perspective, this device requires both a positive supply and a negative supply, which tends to increase

the complexity and cost of the circuit.

H-Bridge Driver

H-bridge configuration is a neat solution to achieve bipolar operation with unipolar supply. Figure 21.51

shows a simple H-bridge circuit driving a load. An H-bridge consists of four transistors that are connected

in a Wheatstone bridge configuration. By turning on/off different pairs of transistors (Q1-Q3) or (Q2-Q4),

bipolar voltage across the load can be achieved using a unipolar supply, see Figure 21.51. In many

applications, the transistors pairs in the H-bridge can be directly driven by the output of a digital device

(TTL or CMOS). The n-p-n or n-channel transistors can be turn on to saturation by a high output from

the digital port and turned off by a low output. If large amount of current is required for the load,

Darlington pairs can be used in place of the individual transistors. Since MOSFETs have larger input

impedance and faster switching characteristics, they are replacing BJTs in almost all switching applications.

Pulse-Width Modulation (PWM)

PWM is one of the more common ways of encoding analog information using digital signal. A PWM

signal is a wave of fixed frequency and varying duty cycle (pulse width). The duty cycle in PWM context

refers to the percentage of time that the signal is in the active state—usually this means a state of logic 1,

see Figure 21.52. In essence, PWM encodes (modulates) the information in the time domain rather than

the voltage domain as with analog signals.

PWM actuation has several advantages over the use of D/A converters and linear components. One

is the efficiency where the switching amplifiers are more efficient than their linear counter parts. Another

FIGURE 21.50 Switching push-pull amplifier.

FIGURE 21.51 H-bridge driver.

Load

−

PUSH

PULL

+V +V

Q3Q4

HLHLLHLH

Load

load

++––

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Actuators 21-31

advantage is there is no need for D/A conversion. Digital signal is maintained from the microprocessor/

microcontroller to the power amplifier. In additional to having better noise rejection capability, this also

reduces the need for a DAC and tends to make the circuit simpler and more cost effective. One drawback

for using PWM and switching amplifiers as a whole is that the high frequency switching induces radio

frequency interference (RFI) and electromagnetic interference (EMI).

The fixed PWM carrier frequency is one main design consideration. Ideally, the PWM frequency should

be high enough to avoid generating audible switching noise, which mean that it should be greater than

20 kHz. However, there are a few factors that put an upper bound on the carrier frequency. Switching losses

of switching devices tends to increase as the switching frequency increases. This reduces the efficiency of

switching components and amplifiers. Higher PWM carrier frequency requires faster switching compo-

nents that cost more. The amount of current going through the device also limits the switching rate. In

general, sub-horsepower devices and office/desktop equipments usually use PWM at 20–40 kHz. For

larger scale industrial applications, the PWM frequency tends to be less than 500 Hz. Another commonly

specified design parameter is the PWM resolution. This is required for generating PWM from a digital

source. The PWM resolution is equivalent to the quantization resolution for ADC. An 8-bit PWM means

that there are 2

= 256 different pulse widths per PWM carrier signal period.

PWMs are widely adopted in the field and almost all microcontrollers and microprocessors have at

least one PWM output port. PWM signal can be easily generated from analog signal by comparing the

analog signal with a periodic triangular signal through a comparator, see Figure 21.53.

21.1.3.6 Interfacing Considerations

We will conclude this section by discussing some issues relating to interfacing between the electrome-

chanical actuator and the power amplification device.

Driving Inductive Load

A majority of the electromechanical actuators use coils (windings) to convert electrical energy to magnetic

energy. From a power driver viewpoint, windings are resistive and inductive loads. Inductors are energy

FIGURE 21.52 Pulse-width modulation signals.

FIGURE 21.53 Generating PWM signal from analog signal.

PWM

OFF

10%

40%

70%

90%

Time

PWM

Duty cycle [%]

100%

PWM

⋅

100%

+ T

OFF

⋅

PWM

Comparator

PWM

Time

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