Week 2

 This week we have started with calculations and some of the members got struggled with installing Multisim. The theory of the LCR circuit has been done as well as the basic formulas theorem. Additionally, the LCR circuit has been built using Multisim. On the other hand, there was a "sustainable development and ethical aspect of the design" assignment next week so the parts of this report have been divided between us, and a deadline has been set for us before the date of the submission so we can gather all the work in one document. Moreover, the bench inspection assignment sections have been divided.  

Goals 

1. Research for both LCR and LR diode circuits (background and theory)
2. Do simulation and build the circuits in Multisim.
3. Divide the bench inspection sections and sustainable development parts.

Background 

Numerous laboratory experiments, computer simulations and mathematical analysis processes have shown that the Chua circuit is the simplest electronic circuit displaying chaos and many known bifurcations phenomena.

The main reason for Chua’s circuit in 1983 came to explain two aspects of the chaos related to Lorenz’s equations in 1963. The first goal was to devise a system through  Lorenz’s equations to show that chaos is a physical phenomenon, and it is not the result of computational approximation errors. The second goal was to demonstrate that Lorenz's attractant produced by computer simulations is chaotic in the accurate mathematical sense.

Theory 

• Expressions for impedance in LCR series circuit

Resistance R, inductance L, and capacitor C are connected in series and an ac voltage 

V= V sin(ωt) is applied across it as shown below.

Since L, C and R are connected in series, the same current flows across them. The voltage across the resistor is in phase with the current, the voltage across the capacitor leads the current by 90 degrees, the voltage across the inductor lags the current by 90 degree. The figure below depicts Vc,  Vl,  Current signal.

The voltage across the capacitor and inductor are in opposite direction. Therefore, the resultant potential difference = Vl-Vc (if Vl < Vc). The phase diagram below shows the resultant for Vr and the potential difference.

Simulation

• LCR simulations

First simulating LCR circuit with L=1mH, C=4pF, R=1kΩ (4pF used as it is the diode capacitance of the D1N4148 capacitor used in circuit 2)

Comment on the use of 4pF capacitor: The 4pF capacitor will be fine to use for simulation purposes but if the circuit was built in the lab a diode with a larger capacitance would need to be used. The reason for this is that the stray capacitance for components on an SK10 breadboard is of the order 2-3pF meaning if it would affect the resonant frequency of the circuit and as this is almost the value of the capacitor used in the circuit it would have a large effect on the circuit.

(LCR circuit has been build using NI Multisim 14.2)

V= 1mV, f= 1KHz, L= 1mH, C= 4pF and R= 1kohm

AC sweep performed at point labeled v:

Difficulties

• Installing Multisim

Next Week 

• Have more simulations
• Do some work for both blog and poster