EE3300/EE5300 Electronics Applications

Week 4 Self-Study Notes

Power amplifiers

A power amplifier is an amplifier designed to deliver significant power to a load. The major considerations in power amplifier design are efficiency and linearity (minimal distortion).

Efficiency refers to the proportion of total power input that is delivered to the load, as opposed to being dissipated as heat in the amplifier itself.

Linearity refers to the ability of the amplifier to accurately reproduce the input signal at the output without distortion. It can be a challenge because power amplifiers often require large voltage swings for which the transistor behaviour is not well approximated by small signal models. This means that the transistor characteristics are non-linear and hence power amplifiers often use feedback to correct for the underlying non-linearity of the transistors.

The concept of a load line

A “load line” shows how the current and voltage across a transistor vary. For example, consider the amplifier shown in Figure 1.

The equation for the load line can be derived using KVL from the power supply to ground through the transistor. Often we draw separate load lines for the DC and AC (signal) behaviour.

The DC load line equation for the circuit in Figure 1 is

where is the collector current. Notice that we considered the capacitors as open-circuits for the DC analysis, which in this case means that is isolated. We also assumed that the base current is negligible compared to the collector current and hence .

Solving for , the load line is

A plot of vs is called the DC load line, as shown in Figure 2. The slope of this line is , i.e. a larger would result in a shallower slope.

The chosen bias point defines how much DC current flows through the transistor when there is no signal input. This is called the Q-point or quiescent point. As shown in Figure 2, the Q-point can be adjusted along the DC load line.

Next, we consider the behaviour for AC signals. We imagine a sinusoidal input signal, although of course the actual signal can be an arbitrary waveform. We assume that the capacitors are large enough that their impedance is negligible at the signal frequency and hence we treat the capacitors as short circuits. Furthermore, all nodes with constant voltage are treated as an AC ground.

These assumptions allow us to simplify the circuit to the one shown in Figure 3.

Notice that for AC signals, the transistor drives in parallel with . To find the AC load line, we write a KVL equation through the transistor. The result is

Notice that we use lower case letters for the AC current and voltage, which we understand to be superimposed on the top of the DC values. Specifically, the total collector current is the sum of the DC and AC components, and similarly for the voltage. We can therefore write and and then substitute into Eq. to obtain

Plotting this equation on the same graph as the DC load line gives the result shown in Figure 4. Notice that is smaller than alone, which means that the AC load line will have a steeper slope compared to the DC load line.

The amplifier cannot have negative or negative because of how the transistor works. Therefore the axis intercepts of the AC load line represent the absolute limits of the output signal. For example, the point labelled in Figure 4 corresponds to zero collector current and is the largest positive swing in .

In reality, the transistor will strongly distort the signal before is reached so an amplifier should not be designed to use this entire range. Hence, load-line analysis is a simplified picture suitable only for quick estimations, and you should perform more detailed analysis using more accurate equations or circuit simulations later in the design process.

Notice that the amplifier cannot output the full supply voltage range . We say that the amplifier does not have rail to rail outputs because it cannot reach the supply rails ( and ground).

Example 1

Use a load line to estimate the maximum peak-to-peak voltage swing that can be delivered to in the circuit shown in Figure 5. Assume that all capacitors are large enough that their impedance at signal frequencies can be neglected.

Solution

Since a load line is an approximate method, we will similarly use fast approximations to find the bias point (Q point). The biasing resistors ( and ) are reasonably small so we expect the current in these resistors to be much larger than , therefore we can use a voltage divider to calculate .

For a rough approximation, we can assume , hence . Therefore by Ohm’s law across we have Since we assume , we have and by Ohm’s law Therefore the quiescent collector-emitter voltage is

To plot the AC load line, write KVL from to ground based on the AC model of this circuit. Recall that the power supply is an AC ground because it has no time variation.

where is the resistance seen between collector and AC ground. Notice that we have neglected the Early effect, as is reasonable for an approximate analysis such as this. Substituting and ,

This equation gives the AC load line. The axis intercepts are

The load line is plotted in Figure 6. We see that there is of headroom to one side and to the other. The smaller of these will limit the output of the amplifier before it clips, hence, the peak output voltage is and the peak-to-peak voltage is .

Remarks about efficiency

This amplifier is capable of large voltage swings, but there is a significant downside. The transistor will run hot! The quiescent current is 150 mA and the quiescent voltage is 9 V. This corresponds to 1.35 W of power being dissipated in the transistor even when there is no input signal. This is a significant amount of power, and motivates us to consider other classes of amplifier.

Amplifier classes

Amplifiers are classified into different classes based on the design of the circuit, and specifically how much of the signal is conducted by each output transistor. The different classes are a trade-off between efficiency and accuracy.

Class A (one output transistor, linear operation)

In a Class A amplifier, there is one output transistor and it conducts for the entire cycle of the signal.

All of the basic amplifiers that we have studied so far are Class A amplifiers, including the common emitter, common base, emitter follower, common source, common gate, and source follower designs.

Class A amplifiers have the following characteristics:

• Low efficiency:

  A class A amplifier wastes power because it continuously conducts the DC bias current. We define the efficiency as

  The useful power is the amplified signal delivered to the load. This is necessarily time-varying, so we write it as . However, it may not be obvious to you why we write on the denominator. The instantaneous power drawn from the voltage supply rises and falls throughout the output waveform’s cycle. However, we define efficiency to be a time-averaged quantity. Hence we define the denominator to be the time-averaged power drawn from the supply, which is a DC quantity because it is constant over time.

  Using the concept of a load line, we can easily evaluate the maximum achievable efficiency for a Class A amplifier. The optimal conditions for a Class A amplifier will occur when is maximised, which means that we want the load to experience the maximum voltage swing.

  This leads to the load line plotted in Figure 7 (a), where the bias point is and the AC load line crosses the horizontal axis at .

  To analyse the efficiency, first we find the time-averaged power drawn from the power supply,

  Also, the AC power delivered to the load has a peak voltage of , which corresponds to a root-mean-square (RMS) value of . Therefore the AC power is

  Hence the overall efficiency is

  Based on this reasoning, 25% efficiency is the highest possible for any Class A amplifier using a resistive load at the collector. For example, if a Class A amplifier drives 50 W into a load, then the total power draw is 200 W. The remaining 150 W is dissipated as heat in the amplifier, making battery powered operation impractical and necessitating heat sinks and fans to provide cooling.

• High accuracy (low distortion):

  Class A amplifiers have the lowest distortion of any type, because the transistor is biased to the middle of its operating range, far from any sharp non-linearities. Hence, Class A amplifiers are the predominant type for small signal applications where the AC power is tiny and hence the poor efficiency can be tolerated.

Class B (the push-pull output stage)

The major problem with Class A amplifiers is the large quiescent current that continually wastes power. To improve efficiency, we must find a way to reduce the quiescent current.

Figure 8 shows how this might be achieved. There is no biasing and hence no quiescent current. Assuming and balanced transistors, then in the absence of any driving voltage, naturally sits at 0 V.

You might recall this circuit from Week 1’s practical, where it was used in the output stage of the homemade op-amp. It is simply two emitter followers connected back-to-back. Each one only begins to conduct once is large enough to forward bias its respective base-emitter junction. For instance, Q1 will conduct when , while Q2 will conduct when .

The push-pull network is a voltage follower with gain , except for the crossover distortion.

The defining characteristic of a Class B amplifier is that it has two output transistors, each conducting for half of the cycle. The key properties of Class B amplifiers are:

• High efficiency:

  You will show in tutorial questions that the maximum efficiency of this configuration is , which is clearly much better than the theoretical maximum of 25% for Class A.

• Crossover distortion:

  The crossover distortion shown in Figure 8 (c) is a major drawback of this design. Notice however that the crossover distortion is only a problem for signals that gradually cross zero. For example, a square wave will quickly transition from one transistor to the other, and so the dead zone close to zero is not a problem. This type of driving circuit is common for digital logic signals, such as the GPIO pins on a microcontroller, although in that case it would use CMOS transistors rather than bipolar transistors.

Class AB (push-pull with reduced crossover distortion)

The Class AB amplifier is a hybrid between a Class A and a Class B amplifier. There is some biasing (like Class A) except that the bias point is kept quite low (like Class B). The precise definition is that Class A conducts for the full cycle (360°), Class B for half a cycle (180°), and Class AB for any amount in between 180° and 360°.

The idea is to bias one the output transistors in such a way that their base voltages differ by at least . This ensures that there is no dead zone where both transistors are turned off. This can be achieved using diodes, whose forward bias voltage is relatively constant, as shown in Figure 9.

The diodes must have a voltage drop that matches the of each transistor, which can be achieved if the diodes are actually transistors whose characteristics are well matched to and , respectively. Hence, these would be implemented using the diode-connected transistor configuration as shown in green.

If there is concern about the diode-connected transistors providing enough of a voltage drop, then a third transistor can also be added.

Class D (digitally controlled pulse width modulation)

A completely different approach to power amplification is the Class D amplifier. You might imagine the “D” standing for “digital”, where the key idea is to use pulse width modulation rather than linearly varying the output amplitude.

Battery powered devices often use Class D amplifiers because of their power efficiency.

Power semiconductor devices

Power transistors

A power MOSFET is a MOSFET designed to handle large voltages and currents. Unlike their small-signal counterparts, power transistors have several distinctive characteristics:

• High current handling capability (ranging from several amps to hundreds of amps).
• High voltage capability (up to several thousand volts).
• Improved thermal management (larger physical dimensions and specialised packaging to facilitate heat dissipation).

An important trade-off in power MOSFET selection is between (on resistance) and the capacitances , , and (input, output, and reverse transfer capacitances). Refer to Week 2 for the definitions of these capacitances. Achieving a low on resistance requires using a large parallel area, but this comes at a cost of increasing the capacitance and required gate charge.

Insulated-gate bipolar transistors (IGBTs)

An insulated-gate bipolar transistor (IGBT) is a MOSFET-BJT hybrid, combining the input characteristics of a MOSFET (zero gate current at DC) with the output characteristics of a BJT (fixed saturation voltage rather than acting like a resistor). At high currents, the fixed saturation voltage of an IGBT is advantageous because a MOSFET will experience a larger voltage drop based on its resistance.

Unlike a MOSFET, an IGBT has no inherent body diode. Often an equivalent diode (shown in blue in Figure 10b) is included in the package to protect against reverse voltages.

Thyristors and silicon controlled rectifiers (SCRs)

A thyristor is a four-layer semiconductor device with alternating layers of P and N type material. The most common thyristor is a device called a silicon controlled rectifier (SCR).

The structure, symbol, and behaviour of a silicon controlled rectifier is shown in Figure 11.

An SCR can be thought of as a robust diode that doesn’t start to conduct until a trigger condition occurs. As shown in Figure 11 (c), the SCR has an “off” state where it will not conduct even if forward biased.

The SCR can be triggered to the on state by applying a positive voltage pulse to the gate terminal. The gate-cathode (G-K) interface is a P-N junction and will be triggered into conduction by at room temperature (with the threshold varying with temperature). The trigger condition can also be characterised in terms of the gate current, and SCR datasheets will often specify both a current and voltage threshold.

Once triggered, the SCR will continue to conduct even if the gate drive is removed. The only way to stop the SCR from conducting is to lower the current below a threshold called the holding current.

SCRs are common in applications where it’s desirable to adjust the amount of AC power delivered to a load by switching the load on for only part of the AC waveform. You might find an SCR in a fan speed controller or light dimmer, for example.

Figure 12 shows an example circuit. The resistors R1, R2 (a potentiometer) and R3 determine the trigger point. Once the SCR turns on, it continues to conduct until the AC current falls below the device’s holding current. In this configuration, it remains turned off for the entire negative half of the AC waveform. A full-wave rectifier could be used to take advantage of the other half of the AC cycle. The diodes D1 and the optional D2 protect the SCR from reverse voltages, because otherwise its gate-cathode junction would be exposed to the full AC peak voltage during the negative half-cycle. Such a circuit is very cheap but introduces significant distortion to the AC waveform, since the load is only powered for part of the cycle.

We will investigate another application of the SCR in the “crowbar” circuit, described below.

Protection

Protection circuits are designed to shut off or limit the power when it would otherwise exceed the safe operating limits of a device. These are features that electronics designers can incorporate to make their devices more robust.

It’s particularly important to consider protection at the input and output stages of your device. For instance, your device’s power source may have the wrong voltage or wrong polarity. Your device’s inputs may be driven to an unexpected high voltage. Also, on the output side, your device may experience a short-circuit condition or even have its output driven by an external voltage.

Power supply polarity protection

Most electronics would be damaged if their DC power supply was connected with the wrong polarity. This can easily happen, for example by connecting a battery the wrong way around.

The simplest and most obvious protection circuit is to use a diode to prevent reverse current flow (Figure 13). You need to choose a diode that can handle the full current flow in the forward direction and can withstand the full voltage in reverse. Another problem is that the diode will drop some voltage, which may be unacceptable if the input voltage is already low.

If the voltage drop across the diode is unacceptable, the one possible variation is to use a diode in the shunt position (Figure 14). There is no voltage loss in the case of the normal polarity. If the power supply is connected backwards, then the diode will short it out, hopefully protecting the rest of the circuit. The diode must be capable of withstanding the short-circuit supply current, which may be much larger than the normal operating current.

A crude short-circuit of the power supply is rather unfriendly behaviour. A more sophisticated approach is shown in Figure 15. When the circuit is initially connected, the load is powered through the body diode of the P-channel MOSFET. The body diode continues conducting until becomes sufficiently negative that the transistor begins to conduct. The large will drive the transistor hard into saturation, providing a low resistance path for the current.

The transistor should be chosen to prioritise low over other characteristics (i.e. it is acceptable to have a large input capacitance for this application). An example transistor to choose would be the IRF4905, which has an of just 20 mΩ. However, that same transistor also has an absolute maximum of 20 V, so if the power supply exceeds that level, then the modification shown in Figure 15 (b) is necessary.

The Zener diode D1 limits the gate-source voltage to a safe level. R1 should be relatively small to ensure a fast turn-on given the large gate capacitance of the MOSFET. The resistor R2 ensures that the gate is discharged when the power is disconnected to prevent any residual conduction if the battery is quickly incorrectly reconnected.

Voltage clipping circuits

Diodes may be used to protect against over- and under-voltage conditions. This type of circuit is useful when you receive a communication signal from outside your device (e.g. when sending a digital or analog signal over a long cable).

The simplest approaches are based on diodes, as shown in Figure 16.

The SCR crowbar circuit

A “crowbar” circuit is a type of protection circuit that attempts to completely short the power supply once it is triggered. This is distinct from a clipping circuit, which merely attempts to limit the voltage. In contrast, a crowbar is more aggressive and will hold the power rail in a short circuit condition indefinitely (until all power is removed and the circuit is reset). It is assumed that the upstream power supply will handle the short condition by tripping a circuit breaker, blowing a fuse, or otherwise detecting the fault condition.

Current limiting for transistor outputs

Consider the Class AB amplifier shown in Figure 18 (a). A short circuit from to ground would cause a large current to flow in Q2 or Q3.

The fix, as shown in Figure 18 (b), is to turn off the output transistors when their output current exceeds a threshold. It works as follows. Too large a current flowing in R1 generates enough voltage to run Q4 on, which in turn “steals” base drive from the power transistor Q2. The current limit is determined by choosing a suitable value of R1 that its voltage drop will approach 0.7 V when the current limit is reached.

The low voltage side (Q3) has a mirror reflection of the same circuit.