# I . Review of Fundamentals Related to DC Power Supply Design and Linear Regulators

**1.1 Introduction**

All electronic circuits require a clean and constant voltage DC power supply. However, the energy source available for the system may be a commercial AC supply, a battery pack, or a combination of the two. In some special cases, this energy source may be another DC bus within the system or the universal serial bus (USB) port of a laptop. In a successful total system design exercise, the power supply should not be considered as an afterthought or the final stage of the design process, because it is the most vital part of a system for reliable performance under worst-case circumstances. Another serious consideration in system design is the total weight and the volume, and this can be very much dependent on the power supply and the power management system. Also, it is important for design engineers to keep in mind that the power supply design may entail many analog design concepts.

Most power supply design issues are due to resource and component limitations within the power supply and the power management system. Nonideal components—particularly, passives, commercial limitations to allocate sufficient backup energy storage within the battery pack, unexpected surges and transients from the commercial AC supply, and the fast load current transients—can create extreme and unexpected conditions within the system unless the power management system adequately addresses all the possible worst cases at an early design stage. Many product design experts choose to have the power supply and the power management system designed at an early stage with esti-mated parameters, with the actual system blocks powered from the system power supply. This approach may help minimize late-stage disasters in a large design project.

In the 1960s and early 1970s, power supplies were linear designs with efficiencies in the range of 30%–50%. With the introduction of switching techniques in the 1980s, this rose to 60%–80%. In the mid-1980s, power densities were about 50 W/in3. With the introduction of resonant converter techniques in the 1990s, this was increased to

100 W/in3 [1, 2]. When high-speed and power-hungry processors were introduced dur-ing the mid-1990s, much attention was focused on transient response, and industry trends were to mix linear and switching systems to obtain the best of both worlds. Low-dropout (LDO) regulators were introduced to power noise-sensitive and fast transient loads in many portable products. In the late 1990s, power management and digital con-trol concepts and many advanced approaches were introduced into the power supply and overall power management [3].

In this chapter we consider simple fundamentals related to an unregulated DC power supply and simple calculations to select the important components, with simple linear regulator concepts gradually extending to a discussion on LDOs. Because of space con-straints, for detailed theoretical aspects and deeper design considerations, the reader is referred to the many useful references cited herein.

**1.2 Simple Unregulated DC Power Supply and Estimating the Essential Component Values**

In a DC power supply derived from the commercial AC source we can have two fundamental approaches: (a) transformer isolated and (b) nontransformer isolated. Transformer-isolated power supplies are safer, but bulky due their its line frequency transformer. This was the case for older electronic equipment where size was not a major concern, and still this approach is used in safety-critical applications or where common mode noise (discussed in Chapter 8) is a serious concern. Classic example in the modern scenario is the high-fidelity music systems. When the regulatory require-ments for electrical isolation are covered by the DC- DC converters followed by the unregulated DC power supply, direct rectification and smoothing are used. One com-mon example is the desktop computer power supplies (known as the “silver box”). In these incoming lines, voltage is directly rectified and filtered by a smoothing capaci-tor rated above the value of peak value of the AC line voltage, which is either 165 VDC (for 120 V, 60 Hz systems) or 325 VDC (for 230 V, 50 Hz). Figure 1.1 indicates the concept.

Given the case in Figure 1.1(c), if the peak voltage of the waveform of line frequency, *f*, appearing at the input of the bridge rectifier is* V** _{peak}*, the peak-to-peak ripple voltage at the output could be approximated by,

(1.1)

Considering the capacitor is ideal, and the forward voltage drop for each of diodes is *V** _{D}*, the approximate output DC voltage,

*V*

*, will be,*

_{DC}(1.2)

*Review of Fundamentals*

**Figure 1.1 **Unregulated power supply derived from the commercial AC line: (a) transformer isolated; (b) nontransformer isolated direct rectification; (c) estimating the size of the smoothing capacitor.

These approximate relationships allow us to estimate the approximate design param-eters for an unregulated DC power supply, with or without a transformer. In the case of an ideal transformer with a turns ratio of *n*, and the input AC line RMS voltage is *V** _{rms}*,

(1.3)

Given the practical situations of path resistances, diode dynamic resistances, the equiva-lent series resistance (ESR) of the smoothing capacitor and the like, and any losses in the transformer, an unregulated DC power supply will have a load regulation curve as per Figure 1.2.

**1.3 Linear Regulators**

Given the case of Figure 1.2, an unregulated DC power supply needs further improve-ments to make the output DC voltage constant at different load current. Historically, with the availability of semiconductor components such as diodes and transistors, linear regulator techniques were developed to solve this load regulation issue. In the following sections, we discuss the linear regulator techniques in a brief manner to highlight the important considerations in linear regulator designs.

In designing a regulated DC power supply, the designer should consider the output voltage changes due to three important situations: (1) output voltage variations due to load current changes (usually depicted in a load regulation curve), (2) output voltage variations due to input source voltage fluctuations (line regulation curve), and (3) output voltage variations due to temperature variations. To illustrate this let us take a very sim-ple case of a shunt regulator based on a simple zener/avalanche-type diode. In designing a simple power converter of this kind, let us start from some specifications as below:

- Unregulated input voltage range: 7 to 9 V DC
- Regulated output voltage: 5 V
- Maximum output current: 10 mA
- Output resistance of the unregulated input source: 10 Ω

The most simple solution could be the circuit in Figure 1.3 with a single resistor and a zener diode, where the regulated output is available at the terminals of the zener diode. Given such a simple specification, if we are to develop this circuit from simple and basic calculations based on available commercial components, we can develop this circuit using a zener diode such as BZX84C5V1from ON Semiconductor. If we consider the overall circuit in Figure 1.3(a), and the equivalent circuit for the diode in Figure 1.3(b), we can design this circuit to achieve the approximate specifications given above. As the maximum load current expected is 10 mA, we can allow the diode to carry about 2 mA under full load situation. The diode we have chosen above has a nominal zener volt-age of 5.1 at 5 mA, and the data sheet indicates a resistance of 60 Ω. With reference to Figure 1.3(a), we can write the following relationships:

(1.4)

**Figure 1.3 **Simple shunt regulator: (a) basic circuit; (b) simplified equivalent circuit for a breakdown diode such as a zener or an avalanche diode; (c) simplified representation of the power supply using Thevenin’s equivalent circuit.

Based on the design conditions selected in the above paragraph, *R*_{1} can be estimated by applying the worst-case condition of lowest source voltage of 7 V and the case of zener diode taking up the whole current of 12 mA (when no load is connected),

giving a close enough E12 range resistor of 82 Ω.

When the input is at the maximum possible value and the circuit is on no-load condi-tion, worst-case zener current occurs. This worst-case zener current is

This gives a worst-case zener dissipation of (5.1 + 0*.*060*** 26)*** 26 ≈173mW *,* which is well within the data sheet limit. Under this condition the output voltage is approximately 5.1 + 0.060 * 26, which is approximately 6.7 V, and under worst-input voltage and maxi-mum load current, output voltage is approximately 5.1 + 0.060 * 2), which is 5.22 V. This clearly shows that the output voltage can vary over a wide range, around an approximate value of nominal 5 V.

Given the variables in Figure 1.3(a), using basic circuit theory we can estimate the approximate Thevenin’s equivalent circuit parameters of the simple shunt regulator, as shown in Figure 1.3(c). We can derive the Thevenin’s equivalent circuit parameters as:

(1.5)

and

From these relationships, we can clearly see that the impact of input source voltage vari-ations can be minimized by keeping the value of zener impedance, *r** _{z}*, much smaller than the value of (

*R*

_{s}*+ R*

_{1}), and the same criteria applies to minimization of load regulation. However, practical limitations of available diodes make these circuits useful only in very low current circuits. Also one major disadvantage of this kind of a circuit is the very high no-load power dissipation.

Based on the same simple example of the shunt regulator, we can develop a relation-ship for output voltage fluctuations in the form of,

(1.7)

where the coefficient *k* _{1} represents the Thevenin resistance, *R** _{o}*, of the circuit,

*k*2 rep-resents the coefficient representing line regulation, and

*k*

_{3}represents the tempera-ture coefficient of the power supply. If you take the simple example in Figure 1.3(a) for a regulated power supply, when the load current is

*I*

*, output voltage*

_{L}*V*

*can be written as*

_{o}For the simplest case of Figure 1.3(a),

This give,

assuming that rz is a constant value.

For this case,

If the temperature effects on the breakdown voltage can be simplified by *V** _{z}*(

*T*) =

*V*

_{z}_{,nom}(1 +

*k*

*) where*

_{T}T*T*is the absolute temperature,

*k*is the temperature coefficient of the zener, related to the nominal zener voltage,

_{T}*V*

*, at a specified temperature*

_{z,nom}(1.10)

The above discussion leads us to consider selection of devices with appropriate data sheet parameters to get the best possible specifications. For example, if we can select a diode with low *r** _{Z}* compared to the total input path resistance of (

*R*

_{S}*+ R*

_{1}), line regulation coefficient,

*k*

_{2}, can be minimized.

While the above discussion leads us an example to developing suitable input-output relationships for the regulated power supply, if one requires better output regula-tion with higher output current capability, more advanced circuit configurations are required. Figure 1.4 indicates two examples of more improved shunt regulator circuits. In Figure 1.4(a), *R*_{1} and *Z*_{1} act the same as in Figure 1.3, where *R*_{2} and *Z*_{2} act as a pre-regulator. In effect the preregulator provides a lower source resistance to the pair *R*_{1} and *Z*_{1}. Relationships for this circuit can be developed using approximations applied to Equations (1.5) and (1.6). For example, if the preregulator can be developed with the useful relationships as applied to Figure 1.3(a), the second stage sees very approximate Thevenin equivalent circuit with

In effect this creates a condition where the regulator stage sees a near constant input and with a lower source resistance. If we can select the diode *Z*_{1} suitably, we get a more precisely regulated output. More discussion on this kind of circuits is in [1].

When we need to achieve a higher output current capability, a transistor can be added to the basic circuit in Figure 1.3(a), resulting in the case of Figure 1.4(b). For this case, when the transistor is kept in the active mode,

As the load sees the collector and emitter of the transistor, maximum load current is given by

This clearly indicates that it improves the capability by a factor nearly equal to the gain of the transistor.

## 1.3.1 Series Regulators

In all the above shunt regulator circuits, when the output current is zero the transistor/ zener dissipates lot of heat, and these circuits are generally used for low current requirements. In general, series regulator concepts were more attractive to industrial applications and consumer electronics, except for their drawback of low efficiency. Figure 1.5(a) depicts a very simple open-loop-type linear regulator. In general, the output regulated voltage VOut can be approximated by,

Under maximum load condition, if we need to maintain the zener diode voltage at the breakdown value, with a minimum current of IZ, min, current through resistor R1 under maximum load current will be

If the load is removed, the base current gets driven into the zener diode and under that

situation, worst-case current through the resistor R1 will be,

If you neglect the zener diode internal resistance,

In this situation, approximate Thevenin’s equivalent circuit parameters will be

and

where re is one of the transistor T model circuit parameters.

where IS is the saturation current and VT is the thermal voltage of the B-E junction.

Considering the temperature coefficient of the zener, kT,

Given the above simplified analysis, we see that the regulated output has a severe dependency on the value of the VBE and the impact of the base current variations under load conditions. This leads to a case of coefficients in Equation (1.7) given by

where *I** _{S}* is the saturation current and

*V*

*is the nominal voltage of the Zener diode. Given the above simplified analysis, we see that the regulated output has a severe dependency on the value of the load current also, in addition to the zener diode’s temp performance. Having discussed the basic behavior of an open-loop series regulator, we can use Figure 1.5(b) to illustrate the basic elements of a closed-loop linear regulator, which can minimize some of these issues. Similar to the case in open-loop series regulator, the output is regulated by controlling the voltage drop across the series-pass element, a power transistor biased in the linear region. The control circuit compares the sample of the output voltage with a reference source, and changes the on-resistance of the series-pass power transistor.If we consider the op-amp to be ideal, and the reference voltage to be constant at*

_{Z}*V*

*, as far as the op-amp could maintain its basic function,*

_{ref}*V*

*can be given by*

_{out}Given this simple relationship, we see that the circuit behaves much better than the previous cases of linear regulators, as far as the op-amp, and the reference sources are considered ideal. If a nonideal op amp with an open-loop gain of *A** _{OL}* and input resis-tance between the inverting and noninverting inputs is

*R*

*, we can develop the following relationship for an output load current of*

_{in}*I*

*as*

_{L}The power dissipation in the linear regulator is a function of the difference between the input and the output voltage, output load current, and power consumed by control circuits. The power dissipation in the series pass device contributes largely to lower the efficiency of linear regulators compared to switching regulators. Efficiency of a linear regulator can be approximated by

*I** _{Control}* is the current drawn by the control circuits, referred to the input side. This cur-rent is sometimes called the ground pin current (particularly in cases such as the three terminal regulators). This indicates to us that the best possible theoretical efficiency in a linear regulator is given by

The major advantages of linear regulators in comparison with switching regulators are their (a) low noise, (b) transient response to load current fluctuations (output current slew rate), (c) design simplicity, and (d) low cost. However, due to the low efficiency of these circuits they are not attractive to high power requirements with wide differential voltage between the input and output sides. The following sections discuss the specifics of the essential components of a series linear regulator circuit.

**1.3.1.1 Series Pass Device**

There are many different options for a series pass device of a linear regulator circuit, either in the form of a discrete design or in the monolithic IC form. Table 1.1 compares the characteristics of these options, as applicable to integrated circuits. In discrete form of circuits, the current capability could be much higher than the values in Table 1.1, but requires large heat sink to keep the series pass device within safe temperature limits. Two possible circuit configurations are given in Figure 1.6.

**1.3.1.2 Control Circuits**

The control circuit samples the output voltage through a resistive divider, and uses this feedback signal to control an error amplifier’s output to control the resistance of the series pass device. Control circuit characteristics directly affect system bandwidth and the achievable DC regulation. The voltage reference is used for comparison of the output voltage in the control circuit, and primarily governs the steady-state accuracy of the device. The control circuit can be based on an op-amp or a circuit designed with discrete components. This directly governs the output transient response and the stability of the output. More on this will be discussed later. In general the designer should be conscious of the power consumption of the control circuits to get the best efficiency.Any overcurrent or thermal protection needs to be incorporated into the control cir-cuits, and Figure 1.7 indicates a general block diagram.

**1.3.1.3 The Output Capacitor**

The bulk capacitance at the output maintains the output during transients. The out-put capacitor is required in order for the design to meet the specified transient require-ments. As with any control system, the voltage loop has a finite bandwidth and cannot instantaneously respond to a change in load conditions. The supply rail for many of today’s microprocessors cannot vary more than ±100 mV while handling load transients of the order of 5 A with 20 ns rise and fall times. This translates to a current slew rate of 250 A/µs [2].

In order to keep the output voltage within the specified tolerance, sufficient capaci-tance must be provided to source the increased load current throughout the initial por-tion of the transient period. During this time, charge is removed from the capacitor, and its voltage decreases until the control loop can catch the error and correct for the increased current demand. The amount of capacitance used must be sufficient to keep the voltage drop within specifications. Design considerations in the selection of the capacitor value are detailed in [3].