Week 3

 This week we are halfway to finish our project. although the difficulties that we are going through due to the circumstances, we are doing our best to complete the project remotely. This is a very new thing for all of us and we are trying to live with it and continue with our studies. 

Goals

1. Develop both theory and simulation.
2. Create blog 
3. Create first poster draft. 

Theory

• Resonance 

At resonance, the circuit accepts the maximum current from the source as shown in the figure below. this is the reason behind calling the RCL series circuit an "acceptor circuit". while the circuit accepts the maximum current, the impedance will be the minimum as depicts in the second figure. 

Resonance in the LCR ac series circuit happens when the reactance of the inductor and capacitor are equal and opposite so cancel each other out. and the resonant frequency will equal to:

This means that the impedance of the circuit will only equal the resistance 

At the resonant frequency, the voltages which appear across the reactive components can be many times greater than that of the supply. And the factor magnification is called the Q factor.

Derivation of the Q-factor equation:

For capacitor:

using the same procedure to derive the Q-factor from the inductor part of the circuit. 

This can simplify further to have the simplest formula for Q-factor:

Bandwidth:

Simulation

For the inductor, resistor, and diode circuit simulation, the D1N4148 diode will be used as previously stated the reason for this is because it has a diode capacitance of 4pF which Is the value of capacitor that is used to simulate the LCR circuit. The diode diffusion capacitance is caused due to stored charge of minority electrons and minority holes at the depletion region. When a positive voltage is applied to the pn junction electrons in the n region will move to the p region and recombine with holes and holes in the p region will move to the n region creating the depletion region to decrease. When the diode is in reverse bias the pn junction stores charge at the depletion region, in reverse bias the diode will have low resistance and act as conducting plates of a capacitor, the depletion region has a high resistance meaning the diode acts as a parallel plate capacitor. The capacitance in reverse bias changes with the applied voltage, the capacitance of the diode decreases when the reverse bias voltage increases. The diode capacitance formula for reverse bias is:

Where  CT = transition capacitance

 dQ = change in electric charge

                dV = change in voltage 

Small signal analysis (1mV)

Using the same values for Inductor, resistor, voltage, and frequency that have been used for the LCR circuit 1mH, 1kohm, 1mV, and 1kHz respectively. 

An AC sweep of the voltage across the resistor from the frequency 0-1GHz. 

 

Using a cursor to find the resonant frequency:

The simulated resonant frequency of the circuit is found to be 5.15MHz, comparing this to the resonant frequency that was found in the series LCR circuit which was 2.51MHz, the resonant circuit is found to be 2.64MHz higher than the simulated LCR circuit.

Due to the diode only conducting when they are forward bias when the AC is reversed (-ve voltage) the diode conducts half cycles there will be no current flow until the electric field breaks down.

In forward bias, diodes have a dynamic resistance when a sinusoidal AC signal is inputted to the diode, the changing input will shift the instantaneous quiescent point (steady-state DC voltage or current when there is no input signal applied), this then defines a change in voltage and current. This means that the AC resistance of the diode is inversely proportional to the Q point of operation.

Lissajous Analysis:

Use Lissajous analysis to measure the phase difference between the Vin+ and the voltage across the resistor. To do this I will use an oscilloscope and connect the AC voltage source to one channel and the second channel across the resistor. The circuit can be seen below.

Large signal analysis (10V)

The resonant f will be the same as the diode circuit with a 1mV as the resonant frequency is dependent on the inductor and capacitor.

Lissajous Analysis: 

Difficulties 

• Doing all the report remotely
• Creating the blog 
• there are no actual labs to do our work.

Next Week

• Build Chua's Circuit
• Chua's Ciecuit theory