Calculating ESL of a Capacitor

Impedance of Various 100μF Capacitors :


  • The figure tells us that the impedance of a capacitor will decrease monotonically as frequency is increased.

  • In actual practice, the ESR causes the impedance plot to flatten out.

  • As we continue up in frequency, the impedance will start to rise due to the ESL of the capacitor.

  • The location and width of the “knee” will vary with capacitor construction, dielectric and value.

  • This is why we often see larger value capacitors paralleled with smaller values. The smaller value capacitor will typically have lower ESL and continue to “look” like a capacitor higher in frequency.

  • This extends the overall performance of the parallel combination over a wider frequency range.


Reference : From Analog Devices Tutorial

Frequency Characteristics of a 0.1 uf Capacitor :


The impedance matches with ESR at around at around 2 Mhz.

ESL Analysis :

Frequency = 20 Mhz

Capacitance = 0.1 uF

From the frequency equation , ESL = 0.63 nH

 Frequency Characteristics of a 1 uf Capacitor :

The impedance matches with ESR at around at around 8 Mhz.

ESL Analysis :

The impedance matches with ESR at around at around 8 Mhz.

Frequency = 8 Mhz

Capacitance = 1 uF

From the frequency equation , ESL = 0.39 nH


The impedance matches with ESR at around at around 2 Mhz.

ESL Analysis :

Frequency = 2 Mhz

Capacitance = 10 uF

From the frequency equation , ESL = 0.63 nH

Frequency Characteristics of a 10uf Capacitor :


The impedance matches with ESR at around at around 2 Mhz.

ESL Analysis :

Frequency = 2 Mhz

Capacitance = 10 uF

From the frequency equation , ESL = 0.63 nH

Capacitor Graph Reference : Datasheets from Digikey



Lets analysis the following circuit.


This circuit consist of two nodes named as v1 & v2
Consider the input voltage is vin .
Lets say the current ‘i’ is passing through the node v2 .
Then the voltage at the node v2 is given by
Voltage at the node V1 is given by
Then the input voltage vin is given by
Substituting the value of V1 in equation 3 we get,
09    (Equation 4)

Then the current ‘i’ passing through the node V1 is,
76    (Equation 5)

The transfer function (by substituting the value of ‘i’ in equations 1 & 2)

Circuit Analysis



Assume a current ‘i’ flows in a particular direction.

The voltages at the nodes have been named as vin, v1,v2

At node v2 :


At node v1 :


Through SL1 :


At vin :


v1 and v2 in terms of vin :



Circuit Analysis

Circuit Analysis pdf


let us take the above circuit into consideration, with three nodes namely:


and i is the current passing through them.

1. Considering node v2 :


2. Now at node v1 :


3. To determine vin :


4. The current i can written as :


5. v1 and v2 in terms of vin





Stewardship for New Emergence

To me, workshop simply means learning new technologies and technical tools (as I only attended technical workshops) . Stewardship for a New Emergence (by Monica Sharma) was totally new for me & gave different experience.

Sometimes, I failed to listen others due to some background conversations in my head. These conversations created misunderstandings in communication. But, I never thought of how I can let it go. I didn’t even noticed this. But this workshop gave a link to think about that. Yes, the primary steps to solve the problem is to start noticing them and making a conscious choice of let it go. 

Before attending the workshop, I thought someone will come & give lectures. But what I experienced was something higher . They taught the tools as well as created the environment to practice them with a peer(co participant).

Most case, I used to avoid pin pointing the mistakes in one’s work though it is helpful for them to grow. Because I believed in that i am not good enough to give feedback.  This workshop gave some procedure to give feedback for others to grow. It also helped me to see commitments behind the complaints of others and I learnt that the growth happens beyond the comfort zone.

World is extraordinary and filled with many opportunities. Its all about our perspective of seeing the world. So stand up & open your window to get there where you wished to reach in spite of difficulties that may surround you. And remember, confusion & mistakes are birth  place for knowledge & perfection. In the world no one has the power to make me to feel bad without my permission. If I bounded with emotion, it will reduce my energy and can not allow me to further action.” These are the few things I absorbed intensely at workshop & planning to practice in my life.

Most of the things which I learnt in the workshop are not completely new to me or to anyone. But the thing is it stimulates me to think about it consciously which I never did in my past.


Powering up an LED

PoweringUpLED pdf

Powering up an LED ; A useful tool to determine the value of resistors to be used in the circuit.

V = I × R (Ohm’s law)

supply voltage = 5V

resistor used = 2 x 33ohm resistor connected in parallel = 16.5 ohm

to determine current ; I = V / R

5 / 16.5 = 300mA

(Power supply voltage − LED voltage) / current (in amps) = desired resistor value (in ohms)

To calculate the amount of power that the resistor will dissipate;

Power Rule: P = (I × V ) W
If a current I flows through through a given element in your circuit, losing voltage V in the process, then the power dissipated by that circuit element is the product of that current and voltage: P = I × V.

led1 led3


Speede V.2

SpeeDe V.1 -pdf

upgraded features ;

– 12 v battery

– improved LDR sensitivity

changes made ;

– 12 v battery

On Speede v.1 we used 2x 9v batteries, one for driving the arduino board and another for powering the laser. This did not suit the device as it kept on draining up the batteries. Which made us upgraded the battery source to a 12 v rechargeable battery, but the laser and the arduino kit could only handle 9v supply. This made us connect an IC 7809 from the battery source and then supply the components ( ic 7809 simply burns the excess voltage i.e.3 v and provides a supply of 9v as an output)

DSC_0490 DSC_0443 DSC_0444

– improved LDR sensitivity

The LDR’s sensing the laser were affected by external light sources, this compromised Speede’s ability to work in a brighter environment. In order to eliminate this factor, two pvc tubes were fitted around each LDR.

DSC_0447 DSC_0450

Demonstration of Fourier Series using Python Code


In mathematics, a Fourier series is a way to represent a wave-like function as the sum of simple sine waves. More formally, it decomposes any periodic function or periodic signal into the sum of a set of simple oscillating functions, namely sine and cosine with the harmonics of periods. So, Fourier series are used in the analysis of periodic functions.

Fourier Series:
begin{displaymath}A_0 + sum_{n = 1}^{infty} (A_ncos(nx) + B_nsin(nx)).end{displaymath}

begin{displaymath}left{begin{array}{lclr}<br /><br /> a_0 &=& displaystyle frac{1}{2p...<br /><br /> ..._{-pi}^{pi} f(x) sin(nx)dx,& 1 leq n.<br /><br /> end{array}right.end{displaymath}
Here i used python programming tool instead of manual calculation to represent the Fourier
Series with some examples

import numpy as np
import matplotlib.pyplot as plt
resolution = 0.0001
x = np.arange(-np.pi,np.pi,resolution)
square =  np.array(x) ……
See more



Python Output:
>>> a0
0.99998642294279794 (~1)
>>> b1
-0.63661977194539721 (-2/ π)
>>> b3
-0.21220658952264121 (-2/ 3 π)



Capacitor pdf



A capacitor (originally known as a condenser) is a passive two-terminal electrical component used to store energy electro statically in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors (plates) separated by a dielectric (i.e. insulator). The conductors can be thin films, foils or sintered beads of metal or conductive electrolyte, etc. The “non-conducting” dielectric acts to increase the capacitor’s charge capacity. A dielectric can be glass, ceramic, plastic film, air, vacuum, paper, mica, oxide layer etc. Capacitors are widely used as parts of electrical circuits in many common electrical devices. Unlike a resistor, an ideal capacitor does not dissipate energy. Instead, a capacitor stores energy in the form of an electrostatic field between its plates.

When there is a potential difference across the conductors (e.g., when a capacitor is attached across a battery), an electric field develops across the dielectric, causing positive charge +Q to collect on one plate and negative charge −Q to collect on the other plate. If a battery has been attached to a capacitor for a sufficient amount of time, no current can flow through the capacitor. However, if a time-varying voltage is applied across the leads of the capacitor, a displacement current can flow.









Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass. In analogue filter networks, they smooth the output of power supplies. In resonant circuits they tune radios to particular frequencies. In electric power transmission systems, they stabilize voltage and power flow.

An ideal capacitor is wholly characterized by a constant capacitance C, defined as the ratio of charge ±Q on each conductor to the voltage V between them




My Experience at the Workshop


The word Workshop is very common in Auroville. Lots of workshops happen over the course of a year. But I never got the idea of attending any of the workshop(I also dont know why I didnt attend any and probably it never struck me).

Sanjeev then one day told us about a workshop called Stewardship for New Emergence (Monika Sharma’s workshop). He told us that the 1st stage of the workshop is for 9 days(I was like wow! 9 days!) and gave us a form to fill for the workshop. Just looking at the form made me feel that the workshop is going to be intense. Just filling up the form made me think a lot about myself.

The workshop was held over a period of 3 months(3 days a month).

We learnt about 40 tools in these 9 days. All the tools given in the workshop are very much related to everyone’s daily life. Every exercise given in the workshop would have somehow or the other happened in your life but I never have thought about how and why it happened, what I learnt is to differentiate the tools that was given.

For example, there was an exercise about ‘anger’. There are two types of anger(Destructive and Principled). This was the first time I heard about anger being differentiated into two types. All I knew about anger before was shouting and pouring emotions on someone(destructive anger). But after doing this exercise I came to know that sometimes even my anger was not destructive and I was Principled in my anger.

There was tool about ‘complaints’. We all listen to complaints made by others and get bored and agitated. But here i learnt to listen to the committments behind the complaints. It made me look at complaints made by other people on me in a dfiferent angle.

Like this i learnt a lot of new things that are needed for the growth of myself and the people around me. Just attending this 9 days(which was fully worth it) of workshop does not give someone a new life. It is important that I practice all the tools that I have learned.

Overall this workshop was totally a new and a different experience for me personally. I came to know more about myself and I think over these 9 days I have accomplished a New Emergence !!