XMUT303 – Note 10 - 1

XMUT303 Analogue Electronics

Note 10: Power Amplifiers

Topics

• Introduction to power amplifier.

• Classes of power amplifiers.

• Efficiency of power amplifiers.

• Power amplifier circuits improvements.

10.1. Introduction to Power Amplifiers

10.1.1. Power Amplifier

Power amplifiers: Its function is to amplify small input signal to larger output signal.

𝑉𝑜𝑢𝑡 = 𝐴 × 𝑉𝑖𝑛

Where:

𝑉𝑜𝑢𝑡= output signal

𝑉𝑖𝑛= input signal

𝐴 = amplification ratio

XMUT303 – Note 10 - 2

Figure 10.1: A physical example of power amplifier

Note that a large-signal amplifier can also be called a power amplifier.

10.1.2. Anatomy of Power Amplifiers

Power amplifiers are designed to drive low resistances with significant power levels (e.g. Watts to Kilo

Watts).

Typical examples are loudspeakers and antennas, which have impedances of between a few and a few

tens of ’s.

To obtain that much of gain in the power amplifier, it often employs a cascading design arrangement

e.g. a number of stages of amplification, rather than a single stage amplifier.

Figure 10.2: Typical stages in power amplifier

10.1.3. Major Classes of Power Amplifiers

Power amplifiers are divided into several different classes:

Class A: transistor always conducting.

Class B: transistor conducts for half cycle only.

Class AB: transistor always conducts small current.

Class C: transistor conducts for less than half cycle.

Class D: transistors fully on or fully off.

The basic idea of many of these types of power amplifier is to make the power amplifier more efficient.

The main figure of merit is the power amplifier efficiency.

XMUT303 – Note 10 - 3

Figure 10.3: Q-point determination of Class A power amplifier

The class of a power amplifier is determined by the bias which establishes the Q-point.

Figure 10.4: Collector current waveforms of various classes of power amplifier

Collector current waveforms of the power amplifiers or transistors operating in: (a) Class A, (b) Class B,

(c) Class AB, and (d) Class C.

XMUT303 – Note 10 - 4

Figure 10.5: Collector current waveform of Class D power amplifier

Collector current waveforms of the power amplifiers or transistors operating in Class D power amplifier.

10.1.4. Efficiency Rating of Power Amplifiers

The efficiency of the power amplifier is given by this equation:

𝜂 =Power in the Load

Supplied Power

The maximum theoretical efficiency ratings of Class A, Class B, and Class C power amplifiers are shown in

the table below.

Amplifier Max. Efficiency (𝜼𝒎𝒂𝒙)

Class A 25%

Class B 78.5%

Class C/D 99%

Table 10.1: Maximum efficiency of various classes of power amplifier

10.1.5. Circuit Efficiency of Power Amplifier

High efficiency means less heat.

Heat = 𝑃𝑖𝑛 − 𝑃𝑜𝑢𝑡

Efficiency =𝑃𝑜𝑢𝑡𝑃𝑖𝑛

XMUT303 – Note 10 - 5

Figure 10.6: Power dissipations in power amplifier circuit

10.2. Class A Power Amplifier

10.2.1. Class A Power Amplifier

Figure 10.7: Q-point determination of Class A power amplifier

Class A power amplifier has a large quiescent collector current.

XMUT303 – Note 10 - 6

Figure 10.8: Class A power amplifier circuit

For a Class A power amplifier, its base current is:

𝐼𝐵 =𝑉𝐶𝐶𝑅𝐵

=18 V

1.2 k𝛺= 15 mA

So, the current at the collector is:

𝐼𝐶 = 𝛽 × 𝐼𝐵 = 60 × 15 mA = 0.9 A

The saturated current at the load is:

𝐼𝑆𝐴𝑇 =𝑉𝐶𝐶𝑅𝐿

=18 V

12 = 1.5 A

The dissipated power at the collector is:

𝑃𝐶 = 𝑉𝐶𝐸𝐼𝐶 = 7.2 V × 0.9 A = 6.48 W

10.2.2. Class A Power Amplifier Efficiency

A PNP transistor is used as an input stage.

Base-emitter voltage drop of two transistors cancel out each other so, we have zero offset between

input and output.

XMUT303 – Note 10 - 7

Figure 10.9: Audio amplifier application of Class A power amplifier

When there is no signal the power consumption of base resistor and the transistor 𝑄2is:

𝑃𝐷𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑 = 𝑃𝑅𝐵 + 𝑃𝐿𝑜𝑎𝑑 = 𝑉2

𝑅𝐵+ (

𝑉

𝑅𝐿)𝑉𝑜

𝑃𝐷𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑 =(30)2

8 Ω+ (

30

8 Ω) × 15 V ≈ 169 W

This requires a heat sink e.g. a large one and large TO-3 or TO-220 case transistors.

Note that the maximum power dissipation in the amplifier itself occurs under quiescent conditions.

We now calculate the power efficiency of the circuit for a sinusoidal input.

We take the more usual situation where the supply rails are equal in value e.g. ±𝑉𝐶𝐶 .

The output voltage is the same as the input, so if:

𝑉𝑖 = 𝑉𝑜 = 𝑉 cos(𝜔𝑡)

The output power is:

𝑃𝑜 =𝑉2(cos𝜔𝑡)2

𝑅𝐿

The average output power is:

𝑃𝑜 (𝐴𝑣𝑒) =𝑉2

2𝑅𝐿

The power dissipated in 𝑅𝐸 is:

XMUT303 – Note 10 - 8

𝑃𝑅𝐸 =(𝑉 cos(𝜔𝑡) + 𝑉𝐶𝐶)

2

𝑅𝐸

The voltage across 𝑄2 is:

𝑉𝑄2 = 𝑉𝐶𝐶 − 𝑉 cos(𝜔𝑡)

The current in the transistor is:

𝐼𝑄2 =V cos(𝜔𝑡)

𝑅𝐿+𝑉𝐶𝐶 + V cos(𝜔𝑡)

𝑅𝐸

This means the total power consumption is:

𝑃𝑇(𝑡) = 𝑃𝑅𝐸(𝑡) + 𝑃𝑄(𝑡) + 𝑃𝐿(𝑡)

So, the total power consumption is:

𝑃𝑅𝐸(𝑡) =(𝑉𝑐𝑐 + 𝑉 cos(𝜔𝑡))2

𝑅𝐸

𝑃𝑄(𝑡) =(𝑉 cos(𝜔𝑡))2

𝑅𝐿

𝑃𝐿(𝑡) = (𝑉𝑐𝑐 + 𝑉 cos(𝜔𝑡)) [𝑉cos(𝜔𝑡)

𝑅𝐿+(𝑉𝑐𝑐 + 𝑉 cos(𝜔𝑡))

𝑅𝐸]

Solving the previous equation by expanding the terms, it becomes:

𝑃𝑖𝑛 =𝑉2

2𝑅𝐸+𝑉𝑐𝑐2

𝑅𝐸+

𝑉2

2𝑅𝐿−

𝑉2

2𝑅𝐿+𝑉𝑐𝑐2

𝑅𝐸−

𝑉2

2𝑅𝐸=2𝑉𝑐𝑐

2

𝑅𝐸

So, the power efficiency of the Class A power amplifier is:

𝜂 =𝑃𝑜𝑢𝑡𝑃𝑖𝑛

=(𝑉2

2𝑅𝐿)

(2𝑉𝐶𝐶

2

𝑅𝐸)

=1

4(

𝑉2

𝑅𝐸𝑉𝐶𝐶2

𝑅𝐿

)

In general 𝑅𝐸 cannot be any larger than 𝑅𝐿. This is due to 𝑅𝐸 must carry all the load current during

negative output voltages without generating a large voltage drop.

Also 𝑉 cannot be any larger than 𝑉𝐶𝐶 and usually must be somewhat less to avoid transistor saturation

and the associated distortion, so, the efficiency is limited to 25 %. The efficiency achieved in practice is

usually in the range 10–20%.

This is true also for circuits with active biasing rather than the passive RE shown here. For this reason, the

output stages of Class A power amplifier are rarely used in high power applications.

XMUT303 – Note 10 - 9

𝜂 =(𝑉2

𝑅𝐿)

(𝑉𝐶𝐶2

𝑅𝐸)

Figure 10.10: Load connection in Class A power amplifier circuit

10.3. Class B Power Amplifier

10.3.1. Class B Power Amplifier

In a Class B power amplifier, its quiescent power dissipation is zero:

𝑃𝐶 = 𝑉𝐶𝐸 × 𝐼𝐶 = 18 V × 0 A = 0 W

Figure 10.11: Q-point determination of Class B power amplifier

But, the collector signal is too distorted for linear applications.

XMUT303 – Note 10 - 10

Figure 10.12: Input and output waveforms based on a Q-point of Class B power amplifier

10.3.2. Class B Push-Pull Power Amplifier

The complementary-symmetry Class B push-pull power amplifier has acceptable linearity for some

applications.

Figure 10.13: Class B push-pull power amplifier circuit

XMUT303 – Note 10 - 11

Figure 10.14: Q-point determination of Class B push-pull power amplifier

Since the base-emitter junction potential is 0.7 V, there is some crossover distortion.

Figure 10.15: Crossover distortions in Class B push-pull power amplifier

10.3.3. Push-Pull Arrangement (with resistors biasing)

The two transistors have to be complementary.

Similar 𝑉𝐵𝐸 characteristics (e.g. 2N3904, 2N3906).

R2 provides bias to overcome crossover distortion.

But temperature changes change collector current (through 𝑉𝐵𝐸).

Select resistors to set the Q point.

It has to bias diodes of transistors (e.g. 0.7 V) to be on the verge of conduction.

XMUT303 – Note 10 - 12

Figure 10.16: Resistors biasing arrangement in Class B push-pull power amplifier

Biasing resistors are equal.

So, half the supply voltage is dropped across each transistor.

However, difficult to maintain a stable bias point with this circuit due to changes in 𝑉𝐵𝐸 over

temperature changes.

Δ temp−> Δ Q point

A more stable arrangement is by replacing the resistors with diodes.

10.3.4. Diode Biasing

Diode characteristics of 𝐷1 and 𝐷2 are closely matched with β characteristics of transistors to have a

stable bias.

BE junctions of other BJT’s are also used instead of diodes 𝐷1 and 𝐷2.

Sometimes AB amplifiers are referred as Class B.

With diode bias, the bias current through diodes is:

𝐼𝑏𝑖𝑎𝑠 =𝑉𝐶𝐶−2𝑉𝐵𝐸

𝑅

So, the quotient current at the collector is:

𝐼𝐶𝑄 = 𝐼𝑏𝑖𝑎𝑠

XMUT303 – Note 10 - 13

Furthermore, ICQ should be 1-5 % of 𝐼𝐶(𝑆𝑎𝑡).

10.3.5. DC Operation Characteristics

Assume:

Let 𝑅1 = 𝑅2.

Transconductance characteristic of the diode transistors are identical.

Q-point:

𝑉𝐵𝐸1𝑄 ≈ 𝑉𝐵𝐸2𝑄

𝑉𝐶𝐸1𝑄 ≈ 𝑉𝐶𝐸2𝑄

𝑉𝐶1𝑄 ≈ 𝑉𝐶2𝑄

𝑉𝐶𝐶 ≈ 2𝑉𝐶𝐸𝑄

Because both transistors are biased near cut-off:

𝐼𝐶𝑄 = 0

Figure 10.17: Diodes biasing arrangement of Class B push-pull power amplifier

XMUT303 – Note 10 - 14

10.3.6. AC Operation Characteristics

Condition: 𝑉𝑖𝑛 = +𝑣𝑒

When the input (𝑉𝑖𝑛) is positive and 𝑄1 is conducting, current is drawn from the power supply and flows

through 𝑄1 to the load.

Figure 10.18: AC operation of Class B push-pull power amplifier

10.3.6.1. Condition: 𝑽𝒊𝒏 = +𝒗𝒆

When 𝑄1 is cut-off by a negative input, no current can flow from the supply.

At those times, 𝑄2 is conducting and capacitor 𝐶𝐶 discharges through that transistor.

Thus, current flows from the load though 𝐶𝐶 and through 𝑄2 to the ground whenever the input is

negative.

The 𝑅𝐿𝐶𝐶 time constant must be much great than the period of the lowest signal frequency.

The lower cut-off frequency due to 𝐶𝐶 is given by:

𝑓 =1

2𝜋𝑅𝐿𝐶𝐶

10.3.6.2. Condition: Maximum

Both transistor 𝑄1 and 𝑄2 are alternatively driven from near cut-off to near saturation.

𝑄1 →𝑉𝐶𝐶2

⟺ 𝑉𝐶𝐶 and 𝑄2 → 0⟺𝑉𝐶𝐶2

XMUT303 – Note 10 - 15

The peak voltage at the collector-emitter is:

𝑉𝐶𝐸(𝑃𝑒𝑎𝑘) ≈ 𝑉𝐶𝐸𝑄

The quotient voltage at collector-emitter is:

𝑉𝐶𝐸𝑄 ≈𝑉𝐶𝐶2

10.3.7. Power Calculations

The maximum that flows in the collector is:

𝐼𝐶(𝑆𝑎𝑡) =𝑉𝐶𝐸(𝑃𝑒𝑎𝑘)

𝑅𝐿=𝑉𝐶𝐸𝑄𝑅𝐿

=𝑉𝐶𝐶2𝑅𝐿

The total (dc) input power comes from the 𝑉𝐶𝐶 source:

𝑃𝑖(𝑑𝑐) = 𝑉𝐶𝐶𝐼𝐶𝐶

𝐼𝐶𝐶 = 𝐼𝐶(𝐴𝑣𝑒) + 𝐼𝐼

𝐼𝐶𝐶 ≈ 𝐼𝐶(𝐴𝑣𝑒) (𝐼𝐶(𝐴𝑣𝑒) ≫ 𝐼𝐼)

𝑃𝑖(𝑑𝑐) = 𝑉𝐶𝐶𝐼𝐶(𝐴𝑣𝑒)

The total current drawn from the supply is the sum of the average 𝑄1 collector current and the current

through the base circuit of the power amplifier.

Figure 10.19: Collector current waveforms of Class B power amplifier

The average value of the current through the collector of 𝑄1 is given as:

𝐼𝐶(𝐴𝑣𝑒) =1

𝑇∫ 𝐼𝐶𝑑𝑡 =

𝐼𝐶(𝑆𝑎𝑡)

𝜋

𝑇

0

This example is just a standard 𝐼𝑎𝑣𝑒 equation for the half-wave rectifier:

𝑃𝑖(𝑑𝑐) = 𝑉𝐶𝐶 (𝐼𝐶(𝑆𝑎𝑡)

𝜋) =

𝑉𝐶𝐶𝐼𝐶(𝑆𝑎𝑡)

𝜋

XMUT303 – Note 10 - 16

10.3.8. Max Output Power

The AC output power is given as:

𝑃𝑜(𝑎𝑐) = 𝑖𝑐(𝑟𝑚𝑠)𝑉𝑜(𝑟𝑚𝑠) =𝑉𝑜(𝑟𝑚𝑠)2

𝑅𝐿

The maximum output power is:

𝑃𝑜(𝑎𝑐 𝑚𝑎𝑥) = 𝑖𝑐(𝑀𝑎𝑥)(𝑟𝑚𝑠)𝑉𝑜(𝑀𝑎𝑥)(𝑟𝑚𝑠)

𝑃𝑜(𝑎𝑐 𝑚𝑎𝑥) = (𝐼𝐶(𝑆𝑎𝑡)

√2) (𝑉𝐶𝐸𝑄

√2)

𝑃𝑜(𝑎𝑐 𝑚𝑎𝑥) = (𝐼𝐶(𝑆𝑎𝑡)

√2) (

𝑉𝐶𝐶

2√2)

𝑃𝑜(𝑎𝑐 𝑚𝑎𝑥) =𝐼𝐶(𝑆𝑎𝑡)𝑉𝐶𝐶

4

Figure 10.20: Quotient collector current vs. quotient collector-to-emitter voltage

The efficiency of the power amplifier is:

𝜂 =𝑃𝑜(𝑎𝑐)

𝑃𝑜(𝑑𝑐)× 100 % =

(𝐼𝐶(𝑆𝑎𝑡)𝑉𝐶𝐶

4)

(𝑉𝐶𝐶𝐼𝐶(𝑆𝑎𝑡)

𝜋)

× 100 %

Rearranging the equation:

XMUT303 – Note 10 - 17

𝜂 =𝜋

4× 100 % = 79 %

So, the maximum efficiency of the Class A power amplifier (𝜂𝑚𝑎𝑥) is found to be 79 %.

Maximum efficiency occurs when output voltage swing is rail to rail.

The maximum power dissipation occurs at a slightly lower output voltage level resulting in an efficiency

of about 50%.

The crossover distortion of the Class B power amplifier can be further reduced by the application of

negative feedback.

Figure 10.21: Negative feedback in Class B push-pull power amplifier

Find the quiescent collector current and the max efficiency of the power amplifier.

𝐼𝑏𝑖𝑎𝑠 =20 V − 1.4 V

2(3.9 k𝛺)= 2.38 mA

The collector saturation current is:

𝐼𝐶(𝑆𝑎𝑡) =𝑉𝐶𝐸𝑄𝑅𝐿

=10 V

10 𝛺= 1 A

The average value of the half-wave collector current is:

𝐼𝑎𝑣𝑒 =𝐼𝐶(𝑆𝑎𝑡)

𝜋=

1 A

3.14= 0.318 A

The total current drain is:

𝐼𝑑𝑐 = 2.38 mA + 0.318 A = 0.32 A

XMUT303 – Note 10 - 18

Figure 10.22: Biasing arrangements for Class B push-pull power amplifier

The DC input power is:

𝑃𝑑𝑐 = (20 V)(0.32 A) = 6.4 W

The maximum ac output power is:

𝑃𝑜𝑢𝑡(𝑀𝑎𝑥) =MPP2

8𝑅𝐿=

(20 V)2

(8)(10 𝑊)= 5 W

The efficiency of stage is:

𝜂 =𝑃𝑜𝑢𝑡𝑃𝑑𝑐

× 100%

Put values into the equation:

𝜂 = 5 W

6.4 W× 100% = 78.1%

10.4. Class AB Power Amplifier

The idea of the Class AB power amplifier is to modify a Class B power amplifier so that the transistors

are just conducting when the input voltage is zero.

There are several methods of doing this.

The most simple is to use a pair of diodes and a resistor as shown below.

One problem with the Class B and Class AB power amplifiers so far is that they are not thermally stable.

As the transistors heat up, their 𝑉𝐵𝐸 drops, which further increases their collector currents, and hence

their dissipation leading to thermal runaway.

XMUT303 – Note 10 - 19

Figure 10.23: Class AB power amplifier circuit

Small resistors (1 Ω) in series with the two emitters can make the circuit more stable: any increase in

collector current will then reduce 𝑉𝐵𝐸 and hence prevent thermal runaway.

The thermal stability of the circuit is further improved by mounting the diodes on the same heat sink as

the transistors.

This ensures that as 𝑉𝐵𝐸 decreases, so also does the diode voltage, and the current does not increase

10.5. Class C Power Amplifier

10.5.1. Class C Power Amplifier

Class C is established by reverse biasing the base-emitter junction.

XMUT303 – Note 10 - 20

Figure 10.24: Q-point determination of Class C power amplifier

The transistor is off for most of the input cycle and the conduction angle is small.

𝑉𝐵 reverse biases the base-emitter junction.

Figure 10.25: Class C power amplifier circuit

10.5.2. Class C Power Amplifier Waveforms (with tank circuit)

XMUT303 – Note 10 - 21

Figure 10.26: Waveforms in Class C power amplifier

10.6. Class D Power Amplifier

10.6.1. Class D Power Amplifier

Class D power amplifiers: Three transistor’s operating modes:

Figure 10.27: Transistor states in Class D power amplifier

Ideally, PC = 0 in both of these cut-off and saturation modes.

A switch-mode amplifier uses a rectangular input signal to drive power transistors rapidly between cut-

off and saturation.

The efficiency is high, allowing large power outputs from relatively small boards and heat sinks.

They are also called Class D power amplifiers.

XMUT303 – Note 10 - 22

Figure 10.28: Switching driver signal in Class D power amplifier circuit

If the switching frequency is a good deal higher than the signal frequency, a Class D power amplifier is

capable of linear amplification.

Pulse-width modulation and a low-pass filter are often used.

Figure 10.29: Pulse-width modulation (PWM) waveforms for Class D power amplifier

XMUT303 – Note 10 - 23

Figure 2.30: Stages in PWM based audio waveform amplifier

The low-pass filter rejects the switching frequency.

Figure 2.31: Output filter arrangement for Class D power amplifier

10.6.2. Practical Class D Power Amplifier

10.6.2.1. LM4651 Conventional PWM driver

XMUT303 – Note 10 - 24

LM4651 is a conventional Pulse Width Modulation (PWM) driver.

Figure 10.32: LM4651 based Class D amplifier application circuit

In the circuit below is used for driving 150 W load (speakers) audio application.

The circuit consists of a “bridge” design using Insulated Gate Bipolar Transistors (IGBT).

Note that the speaker is not connected to ground.

XMUT303 – Note 10 - 25

Figure 10.33: 150 W load (speakers) Class D audio power amplifier application with LM4651

10.6.2.2. IRS 2092 based Class D Audio Amplifier

IRS2092 is an integrated analogue input Class D audio power amplifier.

It drives a pair of MOSFETs for delivering high voltage ( 100 V) load in an audio application.

Typical use of this circuit is for home theatre and powered speaker applications.

XMUT303 – Note 10 - 26

Figure 10.34: IRS 2092 based Class D audio power amplifier circuit