Behind The Beard

Behind The Beard

Behind the beard,
There's a man,
A man who knows how to woo his woman.
Behind the beard,
There's a father,
A father who loves his daughter.
Behind the beard,
There's a brother,
A brother who protects his sister.
Behind the beard,
There's a friend,
A friend who spreads his arms to help which has no end,
Behind the beard,
There's a child,
A child lost in the wild.
Behind the beard,
There's a soul,
A soul that is very calm and cold.

~Jay Mehta

#No_Shave_November

~Jay Mehta

Operational Amplifier : OpAmp Parameters

INTRODUCTION:

• The operational amplifier is the amplifier which can be used to perform various mathematical operations and find its use in analog computing.
• Basically, it is a multistage amplifier circuit which uses a number of amplifier stages interconnected to each other in a complicated manner.
• It has an exceptionally high voltage gain of around 10^5 or 10^6 dB.
• Circuit symbol of ICuA741 OpAmp.:
  
  
• We can apply input voltage which is to be amplified to any one of the  input terminals while connecting another pin to ground or we can connect the input signal between the two input pins differentially.
• Vcc to OpAmp is connected to positive terminal of one source and –Vee is connected to the negative terminal of another source.
• An ideal OpAmp is expected to amplify the differential signal present between its two input terminals.
• The differential amplifier is used in many applications where the response from DC (Zero hertz frequency) to megahertz is required.

BLOCK DIAGRAM OF A TYPICAL OPAMP:-

• Input Stage: Consist of dual input balanced output. This stage provides the maximum gain to OpAmp and also determine the input impedance value Ri.
• Intermediate stage:- Consist of a dual input unbalanced output. This stage is driven by input stage single ended output.
• Level Shifting Stage:- Due to the direct coupling used between first two stage. The input to this stage is an amplified waveform at some non-zero DC level. Hence, this stage brings to offset back to zero volts with respect to ground.
• Output:- Increases the magnitude of the voltage and current capacity of the OpAmp while lowering the output resistance.

OPAMP INPUT MODES:-

Single Ended Mode: If the input voltage is given at only one of the inputs of the OpAmp , while the other input is grounded then we call such configuration of OpAmp as Single Ended Mode.

Inverting

Non-Inverting

Differential Mode: If the OpAmp is given two voltages with a phase shift (180 degrees) then the difference between the two input is been amplified. Also known as Dual (Double) Ended Mode.

Common Mode: If both the inputs are connected to single input voltage then ideally the output should be zero.

CMRR: Common Mode Rejection Ratio is the ability of the OpAmp to reject the common mode signal. Also known as the figure of merit.

CMRR is the ratio of open loop gain to the common mode gain.

Ideally, its value should be infinity; practically it should be as high as possible.

CMRR = (Av/ Acm) ;

CMRR = 20 log(Av/Acm) dB;

OPAMP PARAMETERS:

Open Loop Gain:

open loop mode of OpAmp is one in which no feedback is provided to the OpAmp.

The gain of the OpAmp in such a mode is called Open Loop Gain.

Mathematically, it is given by

Vo = Av * Vd.

Differential Input Resistance (Ri):

It is also called as input resistance.

It is defined as the equivalent resistance measured at either of the OpAmps input terminals provided other is grounded.

Ri should be as high as possible and ideally, it is considered to be infinity.

For u741A OpAmp it is in few MegaOhms.

For OpAmps with FETs, it goes as high as few thousand GigaOhms.

Output Resistance (Ro):

It is defined as the equivalent resistance as seen from the output terminal of the OpAmp while the input terminals are short-circuited.

Ro is measured with respect to ground.

Ro should be as small as possible and ideally it should be zero. Because this ensures that output voltage regulation works properly and improves current carrying capacity.

Input Capacitance (Ci):

It is defined as the equivalent capacitance measured at either of the input terminals of the OpAmp, provided another input is grounded

Ci should be as low as possible.

Input Offset Voltage (Vios):

Ideally, for zero input voltage, there should be a zero output voltage. But practically it isn’t so.

This is due to the unavoidable imbalance for at differential input block of the OpAmp.

Hence, the voltage required at the input to make the output zero is called input offset voltage.

It is temperature dependent and Vios should be as low as possible. Ideally, it should be zero.

Output Offset Voltage (Voos):

 It is defined as the voltage produced at the output due to the input offset voltage.

A compensation network is used to nullify the effect.

Input Bias Current (Ib):

It is defined as the average of the input currents flowing through the input terminals of the OpAmp.

Ib = ( Ib1 + Ib2 ) / 2.

Ideally, it must be zero and practically it must be as low as possible.

This current does exist due to the finite value of input resistance Ri.

And as the two transistors in the OpAmp aren’t same the currents flowing through the two input terminals are also different.

This value can be reduced to PicoAmperes if we use FET operated OpAmp.

It is a temperature dependent quantity.

Input Offset Current (Iios):

It is defined as the algebraic difference between the currents flowing into its inverting and noninverting terminals.

| Iios | = | Ib1 – Ib2 |.

Ideally, it should be zero; practically it should be as low as possible.

Iios exist due to the unequal currents Ib1 and Ib2 flowing through the terminals of the OpAmp.

FET operated OpAmp give lower values of this current as compared to BJT.

This current is responsible for giving finite output offset voltage.

It is a temperature dependent quantity.

Common Mode Rejection Ratio (CMRR) :

It is defined as the ratio of differential gain to common mode gain.

CMRR = (Av/ Acm) ;

CMRR = 20 log(Av/Acm) dB;

It indicates the capability of OpAmp to reject the common mode signals. Example : Noise.

Generally, it is expressed in dB (decibels).

Ideally, this ratio should be infinite, and practically it needs to be as high as possible.

Power Supply Rejection Ratio (PSRR):

It is defined as the change in input offset voltage to the variation in the supply voltage.

PSRR = (delta) Vios / (delta) V.

Also called as Supply Rejection Ratio (SVRR).

Expressed in microvolts per volts or decibels

Ideally, its value should be zero; practically it should be as low as possible.

Slew Rate (S):

It is defined as the ratio of the maximum rate of change of output voltage to unit time.

It is expressed in volts per microseconds.

S = (delta)Vo / (delta)t. [Vo = max].

Importance of  Slew Rate :

Signifies the capability of the OpAmp to change its output rapidly. Hence, decides the highest frequency of operation without giving any distortions at the output.

Fm = S / 2 * pi * Vm.

It depends on the change in voltage gain. Hence, it is always specified at unity gain.

Ideally, it should be infinite; practically it should be as high as possible.

Bandwidth:

It is defined as the range of frequencies that can be amplified almost equally.

It should be as large as possible

Frequency response should extend right up to zero hertz.

Ideally gain of the OpAmp should be constant from zero to infinite hertz.

Gain Bandwidth Product:

It is defined as the bandwidth of the OpAmp at unity gain.

Also called as

Closed Loop Bandwidth.

Unity Gain Bandwidth.

Small Signal Bandwidth.

Large Signal Voltage Gain:

It is defined as the ratio of output voltage to input differential voltage.

Av = Vo / Vd ; Vd = V1 – V2.

Output Voltage Swing:

It is defined as the maximum positive or negative output voltage of an OpAmp is called saturation voltage.

 + - Vsat = Vo(max).

typically Vsat  =  0.9 * Vcc.

Output Short Current:

OpAmp’s output should never be short-circuited to the ground because if we do so large uncontrolled current flow through OpAmp which could damage it.

To avoid this every OpAmp has an inbuilt short circuit protection circuit which would limit the current to a safer value. Typically it is 25mA.

Parameters	Dependency
Voltage Gain	Supply Voltage, Frequency
Power Consumption	Supply Voltage, Temperature
Input Offset Current	Supply Voltage, Temperature
Common Mode Input Voltage Range	Supply Voltage
Output Voltage Swing	Supply Voltage
Input Resistance	Frequency, Temperature
Output Resistance	Frequency
CMRR	Frequency
Input Bias Current	Temperature
Absolute Power Dissipation	Temperature
Slew Rate	Temperature
Gain Bandwidth Product	Temperature

CHARACTERISTICS OF AN IDEAL OPAMP:

Ri = infinity.

Ro = 0.

Av = infinity.

Bandwidth = infinity.

CMRR = infinity.

Slew Rate = infinity.

Vios = 0.

PSRR = 0.

~Jay Mehta

The First Meet

The First Meet

We met; we had a normal chat,

Yet I sat there blushing,

While she just kept smiling.

We thought it would be an awkward talk,

But we comfortably roam around and walked.

There was no room for silence to enter,

As we had lots to share from our clutter,

I cracked many jokes and puns,

And she laughed at them with all the fun.

She instantly made witty comebacks,

Dumping them into a bag of trash!

Her wittiness impressed me,

Because deep down I knew she did it just for me.

We had a good time, may be the best of it,

Hence, we stood there choking ourselves to say Good Bye!

~Jay Mehta

The Hug

The Hug 

What made you hug me?
This was the question I wanted to ask,
But the answer could break my heart,
Yes! My sisters have hugged me,
You weren’t the first girl,
But you indeed are the one whom I love.
The hug you gave was different than I ever got or I will,
We were drenched due to rains,
And still, your cold arms gave the highest possible warmth,
The touch of your hands to my back and mine to yours,
Made a distinct current flow through my spinal cord!
It was electrifying, it was magnificent.
I never thought a hug from a girl could make me feel so significant. 

~Jay Mehta

THE GIRL

The Girl

There was a girl and then there was me,

I did not know her, neither did she!

We were acquaintances behind the screens,

Yet we started sharing lot of our things.

We shared our past,

We shared our lifestyle.

We knew each other’s interests,

And the stories of exile!

We hadn’t met yet, we did not bump into one another,

It is not the cliché that you would ever wonder.

We were writing our own stories,

When suddenly we realized that we wrote about each other!!

We did not know yet as to what it was?

But we definitely knew we had given birth to a new relationship.

~JAY MEHTA

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~Jay Mehta

MY BROTHER

My Brother

You have always been my best friend,

You have proved to be the ideal buddy,

I grew up under your light,

And you always stood by me even in the darkest night.

I have been stubborn, I have been unfriendly,

But you never lost your cool and found the solution calmly.

I have always been the immature guy,

 But you always understood all my lies.

Be it dusk or dawn you were always there,

Never hesitant to hear my nightmares.

You are my counselor,

You are the who consoles,

You always guided me to overcome all my fears.

It has been a while since you haven’t been by my side,

But I know you are still showering your light,

So, that I can continue to take my strides.

To my brother who is my bestie.

To the brother who cares about me selflessly. 

~Jay Mehta

What Makes A Dad?

What Makes A Dad?

God took the strength of the mountain,
Majesty of a tree,
Warmth of the sun,
The calmness of the sea.
He took the generous soul of nature,
Comforting arm of the night,
Wisdom of the ages,
And the power of the eagle's flight.
He endorsed joy of the morning spring,
Faith of the mustard seed,
Patience of the eternity,
And the depth of a family need.
Then God combined these qualities,
When there was nothing more to add,
He knew his masterpiece was ready,
And so, he named it Dad.

~Jay Mehta

The Remembrance

The Remembrance.

The days have come and passed,

Time has blown way too fast,

I was mesmerized,

And before I could wake up,

I found myself reliving my past.

It seemed I had just entered it,

But it had been long since I was living it.

I remembered each folly I made,

 The mistakes that were corrected,

I inculcated the lessons I learned,

I remembered the hand that had been burned.

I was missing all the teachers caring,

I missed the friends who were tricksters.

That was the most carefree time,

That came back with a wonderful chime.

I wished to live that life again,

But that would just be so lame.

Hence, I made a new wish,

And asked for more such memories that I could cherish.

~ Jay Mehta

~Jay Mehta

The Day I Woke Up !

This poem was written by me when I was in ninth grade. It might not be that impressive but me being in ninth grade writing this meant a lot to me and my parents. It was appreciated by my class teacher who even was my English teacher back then. I would like to acknowledge my mentor Mrs. Nandita Ganguly who also appreciated my work and kept me motivated to keep on writing stuff that interested me.

THE DAY I WOKE UP

The days were cool,

And nights were easy,

I just thought of some tools,

And my life became busy.

With a sigh of laziness,

I found the world very hard,

Because I was crazy, for the card.

This made all the difference,

I challenged my appearance,

Until the day had come,

When I woke up.

To jump to reach newer heights,

I had already taken the eagle’s flight.

Things looked colorful,

And surroundings turned bright.

I got my destiny, I reserved all my rights.

My life became honorable,

When a book got my label.

By Jay Mehta.

~Jay Mehta