(2.1)

CHAPTER 2

REVIEW OF RELATED LITERATURE

2.1 Oscillators

An oscillator is a negative feedback system that is shown by Figure 3.1

with transfer function given on Eq 2.1. .A simple oscillator usually produces a

periodic output in voltages. Given that a negative feedback produces oscillation,

an oscillator is basically an ineffective feedback amplifier. [1]

Figure 2.1 Model of negative feedback oscillator system

VoutVin

(s )= H (s)1+ βH (s )

2.1.1 Berkhausen Criteria

The Berkhausen criteria is the condition of whether a circuit will oscillate

or not. It applies to linear circuits with a feedback loop. It states that if A is the

gain of an amplifying element, and β(jω) is the transfer function of the feedback

path, then  βA is the loop gain of the feedback loop of the circuit. The circuit will

sustain its oscillation when:[1]

a. The loop gain is equal to unity in absolute magnitude. And,

b. The phase shift around the loop is zero or an integer multiple of 2π

Figure 2.2 Block Diagram of a feedback oscillator circuit where the Berkhausen

criterion applies.

2.1.2 Ring Oscillators

Ring oscillators consists of three or more gain stages where each stage is

introducing an additional pole and thus giving a 90 degree phase shift in the

closed loop transfer function. An implementation of a ring oscillator can be seen

in Figure 2.3 with its feedback model in Figure 2.4.[2]

Figure 2.3 Cascading common source staged of a ring oscillator

Figure 2.4 Model of a three stage ring oscillator.

(2.2)

A major advantage of ring oscillators is its lack of passive elements. But

this aspect of the ring oscillator comes with the drawback of not having any

filtering or phase noise reduction of the output signal.

2.1.3 LC Oscillators

LC oscillators are made of paralleled combination of an inductor and

capacitor with accompanying active circuit which negates the losses in the passive

elements. The LC combination forms what is called an LC tank. It resonates at the

frequency shown on Eq. 2.2[2]

ωo=1

√ LC

During this frequency, the impedance of the inductor and the impedance of

the capacitor are equal in absolute values but opposite in sign, making the

oscillator tank impedance infinite. In reality, LC tanks have series resistances and

parasitics. Figure 2.5 shows an accurate representation of an actual LC tank

circuit.

Figure 2.5 Tank representation of with parallel resistance

2.1.4 Cross Coupled NMOS-PMOS Oscillator

NMOS-PMOS pair adds another pair of MOS on top of the NMOS-only

oscillator shown in Figure 2.6. Compared to NMOS-only oscillators, NMOS-

PMOS has double output amplitude due to its combination of PMOS and NMOS.

When the left NMOS is off and the right NMOS carries the bias, the opposite

happens to the PMOS, The left PMOS carries the bias while the right PMOS is

off. The flow of the current bias goes through the right NMOS passing through the

tank and then going through the left PMOS before going to the ground. Not like

the NMOS-only Oscillator where only the right NMOS carries the bias current.

This results in the NMOS-PMOS Oscillator to have double of the output

magnitude. Doubling the output magnitude greatly helps to improve the Signal-to-

Noise ratio (SNR) and the phase noise characteristic. NMOS-PMOS, as stated

before, also has less current consumption when compared to its NMOS-only

counterpart because of it having 2 Gm values.[2]

Figure 2.6 NMOS-PMOS cross coupled oscillator

(2.3)

2.2 Inductors

Inductors are a vital part of VCOs since the Q factor of the LC tank circuit

is very dependent on it. The schematic symbol of an inductor is shown in Figure

2.7. In CMOS process technology, the implementation of an inductor is in the

form of a spiral inductor. An example of a spiral inductor is shown in Figure 2.8

Figure 2.7 Schematic symbol of an inductor

Figure 2.8 Square shaped spiral inductor layout

2.2.1 Q-Factor

An inductor’s Q factor is dictated by the ratio of energy stored over the

loss of energy over time. In oscillator analysis, a high Q factor means that the

energy loss is small thus the oscillations move more slowly.[2][3]

Q=ωenergy stored

average power dissipated

2.2.2 Passive Inductors

Passive inductors, in CMOS implementation, is a spiral shaped construct

usually in a square, circular or octagonal form. The main problem for this type of

inductor is its difficulty in construction as well as the measurement of its exact

value in during chip implementation. Another one of its disadvantage is that is

uses a very large area. When looking at a regular LC-tank circuit, one could see

the passive inductor’s image very clearly. Figure 2.8 shows a square shaped spiral

inductor. Figure 2.9 and 2.10 shows an octagonal and circular spiral respectively

Figure 2.9 An octagonal spiral inductor

Figure 2.10 A Circular spiral inductor

2.2.3 Active Inductors

Active inductors are CMOS based inductors. Compared to passive

inductors, active inductor occupy a much lesser area during chip implementation.

Figure 2.11 shows a VCO using active inductors. A traditional active inductor

follows a gyrator topology based on operational transconductance amplifiers

shown in Figure 2.12[4][5]

Figure 2.11 VCO topology using active inductor

Figure 2.12 OTA based gyrator

2.3 DC/DC Converter

A DC/DC converter is a type of circuit that converts a DC from one

voltage level to another. A DC/DC converter is especially useful in portable

devices where different blocks of circuits demanding different voltage level but

only has one battery. Example of a DC/DC converter is a Buck Converter and a

Boost Converter. A buck converter is a step-down converter while a boost

converter is a step-up converter. A Buck-Boost Converter also exists. The

operation of a Buck-Boost converter is as follows: Refer to Figure 2.11 for the

operation descriptions.

a. While on the ON state, the voltage input source is connected to the

inductor. This causes an accumulation of energy in the inductor. In this

state, the capacitor provides a supply to the load

b. While on the OFF state, the inductor is connected to the output load

and capacitor, therefore energy is passed from the inductor to the

capacitor and then to the load

Figure 2.11 Buck-Boost Converter operation schematic