Oscilator Basics

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Oscillator Basics Tutorial
J P Silver E-mail: john@rfic.co.uk

ABSTRACT
This paper discusses the basics of oscillator design including the parameters effecting oscillator performance, with special emphasis on the causes of phase noise. Theory is given for the two types of oscillator topography namely feedback and reflection oscillators.

the device, which is not far fromthe 1dB compression point. A diagram of a typical compression characteristic, for the device used as an amplifier, is shown below in Figure 1.
Output power Saturated output power

INTRODUCTION
This tutorial shows how device parameters can effect the performance of oscillators, including output power, oscillating frequency and probably most important of all – phase noise. An example is given foreach of the two types of oscillator the feedback oscillator and the reflection oscillator

1dB compression point 1dB

Input power

OSCILLATOR SPECIFICATION
OSCILLATOR FREQUENCY The frequency of operation determines the active device to be used as well as the technology. For example, a UHF oscillator would use a device with an fT of a few GHz and would employ a lumped resonator. It would beimpracticable to use a dielectric resonator due to size at UHF frequencies. The use of a very high fT device may lead to problems with stability. OSCILLATOR BANDWIDTH Many applications require variable frequency operation for use in synthesisers where a range of frequencies or frequency steps may be needed across a particular band of frequencies. In order to achieve such variations the resonatormust to have a variable element, which is often a varactor diode (a device whose depletion layer width and hence its value of capacitance, is directly controlled by the amount of reverse bias applied). The use of varactors can cause problems in that they usually determines the Q of the resonator, which is an important factor in setting the phase noise floor, as we shall see later. OUTPUT POWER Theoutput power requirement is determined by the application, but the use of a high power device will mean a phase noise performance. After start-up the oscillator will reach a point close to the saturated output power of

Figure 1 Typical compression characteristic of

an amplifier. The diagram shows the compression point occurs when the gain has dropped by 1 dB from the linear region. Thesaturated output power is the maximum power that the amplifier can deliver and occurs several dB’s beyond the 1 dB compression point. The following expressions [1] give empirical formulae for a common-source amplifier output power based on the small signal gain of the device (ie modulus of S21). The objective is to maximise (Pout – Pin) of the amplifier, which is the net useful power to the load:⎛ ⎛ −GPin Pout = Psat ⎜ 1 − exp⎜ ⎜ P ⎜ ⎝ sat ⎝ ⎞⎞ ⎟⎟ ⎟⎟ ⎠⎠

Psat = saturated ouput power G = tuned small signal transducer gain ie S21
2

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Output
Since the objective is to maximise Pout - Pin , we require that as the input power is varied : d (Pout - Pin ) = 0

∂Pout = 1 differentiate Pout w.r.t Pin ∂Pin
⎛ − G Pin ∂Pout = G exp ⎜ ⎜ P ∂Pin ⎝ sat ⎞ ⎟ =1 ⎟ ⎠ ⎞ ⎟=G ⎟ ⎠Amplifier

Resonator

⎛ − G Pin exp ⎜ ⎜ P ⎝ SAT ∴

Pin lnG = Psat G

Figure 2 Schematic of a simple feedback oscillator. The amplifier needs to have enough gain to overcome the loss of the resonator. The output is usually lightly coupled to an attenuator to overcome load-pull problems.
.......... . (1)

From the data sheet the estimated saturated output power is ~ 16.5dBm; S21 Magnitude @ 8GHz2.659
1 LnG ⎞ ⎛ POSC = PSAT ⎜1 − − ⎟ G G ⎠ ⎝
2 ⎛ 1 Ln(2.659 ) ⎞ ⎟ POSC = 16.5⎜1 − − 2 2 ⎟ ⎜ (2.659 ) (2.659 ) ⎠ ⎝

At maximum value of Pout - Pin , the amplifier output is 1⎞ ⎛ = Psat ⎜ 1 − ⎟ G⎠ ⎝

Pout

.......... ... (2)

and the maxiumum oscillator output power is POSC = Pout − Pin Combining equations 1 & 2

POSC = 9.6dBm
POSC 1 lnG ⎞ ⎛ = PSAT ⎜ 1 − − ⎟ G G ⎠ ⎝

Thus, the...