Oscillators are one of the main building blocks of the electronic devices. They work on the principle of oscillation which is a periodic fluctuation between the maximum and minimum value of the quantity. Oscillators mainly consist of two parts: the active circuit and the resonator. In active circuit there are active circuit elements like transistors or op-amps. Capacitors (C), Inductor (L) and resistors (R) makes the resonator and the frequency of the oscillator is determined by the resonator. An oscillator can be designed in many ways and the main types of the oscillators are: RC Oscillator, LC Oscillator, Colpitts, Hartley, Clapp, and Pierce. The main difference of the Voltage controlled oscillator (VCO) from the other oscillator types is the oscillation frequency can be determined by the Vcont voltage. The variable capacitor (varactor) plays the main role here, if the Vcont changes than the capacitance of the varactor changes and this eventually changes the oscillation frequency. There are some crucial points that require attention while designing an oscillator: Stability, Phase Noise, Gain, Q factor, Frequency Pushing and Pulling. In this report the brief information required to design a Colpitts VCO is given and fundamental resources books, internet sources, application and lecture notes is analyzed.
To be able to design a Colpitts VCO some definitions and some knowledge is required to learn. These topics and basic explanations are given; The characteristic and analyses of Colpitts VCO;
Figure 1: Colpitts Oscillator
When there is an unknown two port network, to be able to identify what is inside of this black box we need s-parameters . The figure and the explanation of the waves are given below;
Figure 2: Two port network
Then the scattering matrix is created below;
Frequency pushing is the VCO's sensitivity to supply voltages. Every oscillator needs a power supply which comes from the DC voltage source and the operating frequency of the oscillators is sensitive to this DC power supply. That is to say, as DC voltage changes the output frequency changes. Pushing is expressed in Hz/V and can be negative or positive. Frequency pushing effect can be minimized by using a high-Q resonator or by well-regulated power supply. 
Frequency pulling is the frequency variation caused by changes in the impedance of the output load. In other words, we only measure the output frequency with some impedance at the output of the oscillator and if ZL (output impedance) changes the output frequency also changes. It is usually specified at a load return loss of 12dB and all possible phases, and is expressed in MHz peak-to-peak. Frequency pulling can be minimized by isolating the load from the oscillator. 
This is the slope of the tuning characteristic and is expressed as frequency change per unit voltage change (MHz/V, etc.).
Q factor (Q of the resonator):
Basically Q factor is the ratio of operating frequency to the bandwidth. Q=f0∆f0=ω0∆ω0
The energy loss is inversely proportional to the Q. That is to say, if you have a higher Q, the energy loss is less.
Transmission Line Theory:
To be able to construct an oscillator at RF, transmission theory should also be learned. In the microwave frequency region, power is considered to be in electric and magnetic fields that are guided from one place to another by some physical structure. The physical structures that are guide the power are called Transmission Line. Two wire line, coaxial cable, strip line, microstrip line and slot line are some of the transmission line types.
If the characteristic impedance resistive is not equal to the load impedance, part of the power is reflected back and the...