TECHNICAL RANTS

Of my classic Vacuum Tube Audio Hobby

*"Deep Dive"*

Check your Regulator & BC Vest

PRIOR TO ENTERING THE WATERS BELOW

WHY CLASSIC TUBE AMPS?

Me? well I am all about Reliability & Restoration for safe, daily Tube Amp operation

Not appearances or aesthetics, although I try to restore Classic Gear for better looks when possible

My website is not *one of the "Tubes for the rest of Us" open
arms thing*

My Website, is for Serious Hobbyists who Seek and Find......

Straight talk, Specifics, Facts and Humor.....

Technical subjects they are Technical, no Sugar Coatings....

So I never just answer THE question....

* "I inform and educate"*

So if you want tp keep classic old equipment alive, for future generations

Our past will always teach us something new to Us.

The Past offers clues, So our future can improve

*KNOWING YOUR PAST, WILL AVOID REPEATING IT*

This journey, is about to get Technical

Are you ready for a deep read?

Coffee, Tea, Sharp Mind, Learning Cap

ON MY MATHEMATICAL RANTS

*Math, oh Math, I really believe that the way that Math has been taught is not the best*

*When teaching Math, Teachers should show students real-life examples of
how Math is applied.*

*A storyline of how Math is used, where and when*

*Trigonometry, Geometry, Algebra, Calculus, Differential Equations,
Vector Analysis*

*Mathematical tools, are not a burden.*

*Each subject area in Math is just like a special "toolbox" with
dozens of concepts that each*

*all do one thing very well...*

*Math models and describes our physical & theoretical reality in ways we
can relate to*

*by Scientific measurements, data and the resulting solution*s*
to all types of problems.*

*It wasn't until I took Engineering Courses to apply the Math, a light
bulb turned on.*

**Word Problems get you thinking about the problem, not just the
Math**

*So the next time you drive over a Bridge, think about the people who
did all of the*

*Calculations, to make sure that it would not fall apart and have a
useful service life.*

*So did your Trigonometry Math teacher ever show why you needed Cosine, Sine and
Tangents?*

*Unlikely, unless You had a great Trigonometry teacher.*

*Same for Algebra and Calculus, the symbols mean more than Greek
characters*

*They are life itself made into equations to help solve problems and
understand the*

*world that we live on and in..*

*Me, I was terrible at Math. My scores were always close to failing.*

WAS I GOOD AT MATH?

*I needed special tutoring when I was in 1st and 2nd Grade*

*Could not Add or Subtract, so I would use my fingers under the desk
like a Human Abacus. *

*Multiplication tables were sheer torture.*

*In Middle School I was terrible, in High School somewhat*

*good at Geometry, but struggled with Trigonometry and Algebra.*

*My Math Teacher and Soccer Coach Paul Trittschuh made Math bearable*

*with Humor, but missed the application part.*

*Then.... I studied Electrical Engineering..... *

*When I finally understood how to apply Math, the whole world*

*changed for the better, I now realized how to use the Unit Circle,
take Derivatives*

*to calculate Position, Velocity and Acceleration...*

*Use Integrals to go backwards from Acceleration, to Velocity to
Position.*

*A whole new world opened up.*

*Just as Tom Cruise told Brad Pitt;*

*"Now look at the world with your Vampire Eyes"*

*I saw a different world with my*

*"Mathematical Eyes"*

Something about those "Decibels"

I use decibels often at work, and in this Hobby as well

My career is Radio and RF, so I use decibels alongside my Audio hobby

This is all deliberate, as the decibel shows us how versatile they are in a technical context

So what is a dB?

Well, lets start with two common formulas for expressing Power and Voltage in decibels.

**POWER - Watts**

dBw = 10 log (P_{1}/P_{2})
Power in Watts, Audio Amplifiers, RF Transmitters

*Power is always 10 log*

**VOLTAGE - Volts**

dBv = 20 log (V_{1}/V_{2})
Voltage in Volts, Audio Amplifiers and Preamplifiers

*Voltages are always 20 log*

Logarithms are also cool!

The
log function is Log Base 10, not a Natural LOG, that LN is base *e* (Euler's
Number) symbol is LN

LN Factoid:

Euler was a Swiss Scientist who created/ discovered the natural log.

Natural because it is used to describe the behavior of Nature, the Creation and also Money!

**A QUICK REVIEW OF VOLTAGE AND POWER **

**WITH SOME ADDED CONTEXT **

So Power in Audio is typically expressed in Watts, Milliwatts, not Microwatts or Picowatts

Microwatts and Picowatts are PC Board design level Semiconductor Dissipation levels

Millivolts, Microvolts and Nanovolts are usually in Radio Circuits, and/or Spectrum Analyzers

Watts P_{2} = 1.0w

(Audio Power Amplifiers and RF Transmitters)

Milliwatts P_{2 }= 0.001w

(RF Cell Phone Transmitters and Circuits)

Voltage in what we use in Tube Amps is typically in Volts, Millivolts or Microvolts so some examples below;

Volts are the usual, Millivolts are used in RF Testing of RF Gain Stages, Microvolts are similar to dBm

they are used to measure and test the levels of received Radio Signals in a Radio Receiver

Volts V_{2} = 1.0v

(RF Transmitters & Tube Audio Amplifiers)

Millivolts V_{2} = 0.001v

(RF Receive and Transmit Pre Drivers & Audio Sources, RF Millivoltmeter probes to test/troubleshoot Radio PC Boards)

Microvolts V_{2} = 0.000001v (RF Received Radio Signals, RF Signal
Generators)

The fear of Calculators, what are all those extra buttons for?

On your Calculator just look for a LOG key... if it is absent, don't worry for now...

It is unfortunate that we call those types of Calculators "Scientific" when they should be called

"Complete" and the usual Calculator a.k.a Adding Machine, "Normal".

I think that calling it a *Scientific Calculator* scares regular people away.

Now, the denominator in the dB formula is always your reference, it allows you to calculate

dBw = 10 log (P_{1}/P_{2})

dBv = 20 log (V_{1}/V_{2})

the ratio of two values of Power (P) or Voltage V), resulting in a ratio calculation

Then by using Logarithms and taking the LOG of that Ratio we make a dB

by multiplying the Power x 10 or the Voltage x 20

If you want to know why, Google is your friend...

Ratios

A fraction has a Numerator and a Denominator

Fraction = Numerator (on top) /Denominator (on bottom)

Fraction = 1/2 = 0.5 = half

Fraction = 3/4 = three quarters

Fraction = e/Pi = (2.718281828/3.142857143) =0.864907869

Why did I divide Euler's Number by Pi?

Because I can... that is the Power of Math!

What is 0.86490 good for? Nothing really...unless it had a purpose.

You can do calculations for the Fun of it, just to practice

Just like Rappers Rap for the Fk of it and hope they got it recorded

And people shoot Bullets in the Forest at nothing really....

To have FUN

Egyptian Civil Engineers some 4500 years ago, used Pi, so why don't You?

They made some interesting structures with Pi.

If they used Pi, so can You!!!!

Pi is important to understanding A.C. Mathematics, Capacitors and Inductors...

Math is also symbolic, with little or no numbers.

f(t) = x (t) - y^{2}(t) + z(t)

This is what makes Math tedious, the act of solving equations in isolation.

Getting a right answer, for what?

The missing link to Math anxiety, is calculating numbers without a purpose or a goal.

Just to pass an exam, but we should know why?

Every equation or types of equations should come with an image of what it represents.

And this is the missing link in Math Education today

Just my humble opinion....

Enter the Decibel or dB (applause please!)

That makes dB's user friendly when you get them as your data inputs.

If you only have dB's it's a simple addition and subtraction.

A First Grader can do dB calculations....

Interesting huh?

It gets more interesting when you have the units, like dBm and need to calculate an actual value of Voltage or Power.

Where the m stands for milli, or one thousandth of something, like 0.001, can you solve for the Numerator?

Sure you can, I will show how.

I will take you on an unexpected adventure to calculate Watts or Volts, Milliwatts or Millivolts, Microwatts or Microvolts...

The Metric System is perfect for all of this Math, and when you use dB's you are actually using the Metric System

Just like giving a Baby Cough Medicine, disguised as Cake!

If you insist on Inches, Feet, Miles, that's fine.

But when you start to work with Math... you realize that Calculations in Metric are so-much-simpler

and far-more-intuitive than English units, far more. All you need to do is move a decimal point Left or Right.

Just like you do when you reach in Intersection, you turn Left, Right or keep Straight.

Imagine having to do 1/8 of a turn on Intersection #1, then 3/4 of a turn on Intersection #2.

How many people would pass their Drivers License tests?

Life is Metric, then the English gave us half, then half of a half, then half of that half.

One Sixteenth, One Thirty Second, One Sixty Fourth.

Carpenters are amazing, they still use the English System, that is fine, until things get smaller than 1 Inch.

What is a dB reference value used for?

So the reference in the above dB formulas, is established by the denominator of the fraction;

P_{2}
(Power) or
V_{2 }(Voltage)

Now to be able to calculate the actual value of the Voltage (Volts) or Power (Watts)

You are taking the Log of the ratio of one value to the reference value.

Then multiplying as: Power x 10 and Voltage x 20, look at the two formulas.

The Numerator, is that value you *measure*,
*estimate*,
*imagine*, etc.

When the Numerator is Greater than the Denominator you get GAIN.

When the Numerator is less than the Denominator you get LOSS.

Thus GAIN & LOSS are insights that the dB provides into what you are measuring or comparing.

Hence Mathematical Division is a "comparison" of two numbers, expressions, quantities, etc.

_{The denominator sets the calibration of the formula, establishes the
unit of reference.}

_{A Decibel alone as in 10 dB is qualitatively meaningless, unless you know what it is
being referenced to.}

But, the decibel is always quantitatively significant.

The decibel offers a "magnitude" or size of a measurement, so it can be used to know if it is a big or small thing

by just looking at the magnitude, you know that 10 dB is less than 30 dB. -15 dB is less than 5 dB, and so on.

The sign of the Decibel, it shows the GAIN or LOSS as a magnitude with relation to a reference.

The Numerator is known as the OUTPUT and the denominator as the INPUT or REFERENCE.

It can have two roles Mathematically, depends on how you use the Formula.

The more negative the -dB, the smaller the size of the value of the dB relative to the reference or denominator

The more positive the +dB value the larger the size of the value of the dB relative to the reference or denominator

If the Decibel is zero, that means that the measurement is equal to the reference, the same value.

**Proof of reference Calculation**

**(zero Gain or Loss) **

**Input of 2 milliwatts (denominator) and Output is 2
milliwatts (numerator)**

**How many dB change is that?**

dB = 10 log (2/2)

dB = 10 log (1)

dB = 10 * 0

dB = 0

Where the (log) in base 10 of one (1) is equal to zero, no change.

Put in layman's terms; if I measure a one Milliwatt signal and want to express than in dBm relative to 1 Milliwatt, this is zero dBm or dBm = 0

So Zero dBm means that my (1) Milliwatt signal in dBm is my reference, if you are working in dBm.

**Example of a +3dB difference Calculation **

**(can also be called a "Gain", if Negative -3dB "Loss")**

**If you measure 2 milliwatts in your Circuit Output and your Input
is 1 Milliwatt**

**this indicates (tells you) that your Circuit has a +3 dBm Gain when referenced to 1
Milliwatt.**

dBm = 10 log (2/1)

dBm = 10 log (2)

dBm = 10 x 0.3

dBm = +3

dBm = +3, meaning that 2 milliwatts is twice 1 Milliwatt, +3dB higher than 1 Milliwatt.

**If you measure 0.3 milliwatts in your Circuit Output and your
Input is 1 Milliwatt**

**this indicates (tells you) that your Circuit has a +3 dBm Loss when referenced to 1
Milliwatt.**

dBm = 10 log (.3/1)

dBm = 10 log (.3)

dBm = 10 x 0.3

dBm = -5.22

Your Circuit lost 5.22 dBm as your measured input was 1 Milliwatt and your measured output was 0.3 Milliwatts.

MATHEMATICS IS AWESOME

DON'T GET DISCOURAGED, SOME MATH TEACHERS LOVE MAKING STUDENTS SUFFER

DO NOT GIVE THEM THAT PLEASURE!

SHOW THEM YOU CAN DANCE, SIT DOWN, WORK OUT PROBLEMS

DISCUSS THEM WITH OTHER HOBBYSTS

USE YOUR TUBE AMPS TO TEST

ONCE YOU BECOME GOOD AT TEST EQUIPMENT AND MATHEMATICS

YOU CAN TURN THIS INTO A BUSINESS!

HANG IN THERE!!

*Study hard, and challenge them to show you how to apply the Math they
teach you!*

*Challenge your Teachers, * *show them who you
are... that you are interested*

*Don't give up, Math is that best friend, who you don't invite over often...*

*as when it speaks, you feel uneasy, a bit disoriented.....*

Math is a Universal Language

Music is a Universal Language

So when others ask how many Languages do you speak?

Not One, but Two

If you play an instrument or sing, Three.

I AM AN RF ENGINEER BY TRADE

DO YOU WANT TO LEARN ABOUT CELL PHONES?

A LESSON ON CELLULAR PHONES, (really Dude come on, leave me alone)

MAKING YOU WISER, AS YOU STARE AT THOSE SCREENS

AND MIGHT BE CURIOUS TO KNOW WHAT IS GOING ON

BETWEEN THE PHONE AND THE TOWER IN TERMS OF RF POWER

*(SKIP THIS SECTION IF YOU FEEL QUEAZY, AND COME BACK WHEN READY)*

CELLULAR RADIO AND THE MARKETING ON T.V.

JUST COME WITH US, WE HAVE THE BEST 5G COVERAGE!

So dB's inform you about the amounts of a thing or a measurement, in the previous examples were in milliwatts of dBm

what the dBm is being used for, is relative to a reference of 1 Milliwatt, any Cellular Radio Propagation Engineer knows the dBm.

The dBm is used in Cellular Coverage Map studies.

Those Marketing AT&T vs. T-Mobile Maps, the colors over the US are in dBm.

Just if you are curious when you see the Commercials on TV

Some picky Engineers use dBuV as well but usually the dBm is the universal GEEK code for Cell Coverage signal levels.

I got the Map below online. It looks highly like Marketeering material

The user density of the East users of the US is far greater than the West.

Can you sense some BS here?

I can see one thing, 5G is being deployed first in Dense Urban, so makes sense.

The East Coast area looks a bit light on Coverage, the West seems optimistic

A Cellular Signal above -110 dBm and that is quite weak, but usable, when you drop down to -111 to -118 dBm, that becomes shaky.

Good coverage is -85 dBm to -50 dBm, if you are -45 dBm you are probably less than a mile from the Cell Tower.

Remember 0 dBm, that is 1 Milliwatt. You will never see 0dBm on your Cell Phone as this type of RF Power

would require that you stand 3 meters from the Cell Tower Antenna and expose yourself to an RF Radiation Hazard.

The typical Cell Phone radiates no more than 600 Milliwatts of RF Power then it gets lost through your head, body, car, buildings, etc.

Now that you know the dBm formula you can calculate that in dBm of your iPhone Transmitter max power.

Cell Phones are measured in SAR (Specific Absorption Ratios) and is the maximum RF power allowed when exposed to human flesh.

Do Cell phones cause damage, of course, Coca-Cola causes damage, McDonald's causes damage.....

It is all how we manage the risks of the damage long term. So as we drink bottled water and ingest plastic molecules

we are walking around with Plastic in our bodies. How much of this can cause issues, the jury is still out.

How much damage can a Cell Phone cause, same, the jury is out on this as well.

I don't want to go deep into this subject but the link below are the current SAR limits.

SPECIFIC ABSORPTION RATIO (SAR)

THE MEASURE OF WHAT GOES INTO YOUR BRAIN/BODY

https://www.apple.com/legal/rfexposure/iphone12,5/en/

Back to the 600 Milliwatts;

dBm = 10 log (.6/1)

dBm = 10 log (0.6)

dBm = -2.21 dBm

So if your phone can RECEIVE -110 dBm, and Transmit with a Peak of -2.21 dBm you can see here MAJOR differences in Power.

Delta dBm = -2.21dBm - (-110 dBm) = 107.79 dBm of difference in signal level!

But remember that that -2.21 dBm has to travel miles to a Cell Tower, so when it arrives, it is more like -100 dBm or less.

And the farther you get from the Cell Tower, the lower the dBm until is reaches -115 dBm

and your call drops, or your phone roams for a better Tower

If you want to visualize how this works, just think about it this way.

THE CELL TOWER SCREAMS AT YOUR PHONE (-25 to -70 dBm) then continues to fade away with distance as you get farther.

YOUR PHONE WHISPERS BACK TO THE TOWER (-110 to -70 dBm) then fades away with distance as you get farther.

The Cell Tower has **BIG EARS**
and a **BIG MOUTH**

Your Cell Phone has **SMALL EARS**
and a **QUIET VOICE**

This is an **"Un-Balanced" **System that works

Below a diagram showing the Tower "Shouting" at the iPhone.

The RF signal has lots of enemies along the waym and that Tower is sending

out plenty of RF energy. Imagine that small iPhone with the exact

same obstables in "reverse" and transmissing only Milliwatts of Energy?

Remarkable that the Tower can even understand when the iPhone is Tramsmitting.

The Radio Signal Processing Power of today's 4G/5G systems is amazing.

Heck ebe GSM 2G and WCDMA 3G were cool in their days.

Just like Bell Bottoms and Mullet Haircuts...

But that is how it works, else you would have to carry a Trailer behind your Car with a

$200,000 Cell-on-wheels, to match what those Towers are doing!

*IMPRACTICAL*

*Little do folks know that the old Bag Phones and Car Cell Phones
developed 3 Watts (not 0.6 watts)*

*Back in those days, Cell Phones were quite big and they did not last
very long on Batteries.*

*Having a small Pigtail Antenna on your Vehicle was a Status Symbol,
like Pagers*

*until Drug Dealers started to use Pagers and we went from being a
Doctor to a Thug.*

*A BALANCED SYSTEM YOU HEAR ME I HEAR YOU*

The RF Engineer designs Coverage for a Balanced System, meaning that the RF Power that the Tower sends out

must be in Balance with your iPhone by making the Receivers at the Tower as sensitive as possible.

Else, your iPhone would receive the Tower, but the Tower could not receive your weak signal.

Radio Engineers call this an Unbalanced System.

It's a two way radio the energy in the sky works like this;

*THE TOWER* *SHOUTS AT YOU *

*WITH HIGH POWER *

*THEN SIMULTANEOUSLY*

*UNDERSTANDS AND RECEIVES*

* YOUR LOW POWER WHISPER *

*FROM YOUR SMARTPHONE*

*The Tower has a Big Mouth and Huge Ears*

*Your Smartphone has a Small Mouth and Small Ears*

This is why Cell Tower Receivers are super sensitive and use sophisticated multiple Receive Antenna (RX DIVERSITY) to hear your phones

that* Whisper* at much lower Power, much less, as the 600 Milliwatts
or less is
just the small Transmitter in your iPhone
(or some close value)

By the time that small amount of power leaves your iPhone it has to face losses in the phone's internal Filtering, your Car,Antenna mismatch

so the power starts to fade quickly inside of the phone and then when the phone radiates that power

it fades away as the inverse of the distance to the Tower, starts high, drops low.

Cell Tower Transmitters are usually in the +50 Watt Range, they need to travel through lossy filtering

and then, lossy Coaxial Cable that can lose on the order of -2dB to -5 dB, or more of the power in the lines themselves.

Of course the longer the Coax Cable, the more the loss. Runs of 250 feet are not uncommon

and Higher Frequencies, incurr more losses all around.

The Tower Antennas, they Transmit only the RF energy that makes it to the Antenna Connector from the Base Station.

These coaxial cable losses are now higher as frequencies are much higher in 5G than 4G.

But the new generation Transceivers are up on the Towers, so Coaxial cable losses are now

not a significant part of the Path Loss Calculation.

But ironically 4G-LTE used the 700 MHz Band. but 5G NR enjoys 600 MHz

lower frequency, more coverage.

But the rest of 5G NR can go far above 2 GHz.

https://beebom.com/list-5g-bands-us-verizon-att-sprint-t-mobile/

Again newer generation Cellular Radio System Base Stations place the Transmitter right next to the Antenna on the Tower.

These are called "Main-Remote" Radio Base Stations, I call them practical, as the Coax Cable is just a 10-15 ft. Jumper, not 250 ft.

Public Safety Radio Systems, still use traditional long Coax Cable length's with all of the Radio Gear in a shelter, as the manufacturers

do not find enough funding to transform their infrastructure for smaller physical space and footprints.

Public Safety Radio Systems need temperature controlled shelters usually at the base of the Tower.

While some Cell Towers use Outdoor Cabinets only next to the Tower, super space efficient.

Public Safety Base Station technology lags Cellular, of couse.

As Public Safety systems do not generate CDR (Call detail records) that would be sent to

a billing processor to generate Airtime Bills.... that is the realm of Public Cellular Radio.

We know this well, when we get our Cellular Phone bill and need a college accounting degree to understand it.

NOISE FLOOR, CAN I HEAR YOUR WHISPERS IN THE NOISE?

The Noise Floor in dB of a major US City is in the -100 dBm if lucky, while that Prepper Cabin in the Woods

that takes 5 hours to drive to and has no Cell Tower Coverage, that place can have a Radio Noise Floor below -122 dBm.

The limits of today's modern DSP receivers is -120 dBm, so as long as the Noise Floor is below -120 dBm, the receiver can receive.

Receivers are only as good as the Noise Floor, as You are only as good as the noise in a Bar full of people.

Picture yourself in a noisy Bar with a Band playing trying to listen to that "gorgeous lady" you just met

Over all of the Music and the Noise, you struggle to understand the words among the noise.

This is what a Cellular Site Receiver has to deal with, smack in the middle of for example; New York City.

Cell Phone Systems have enemies like Noise, Interference and Obstacles like Buildings, Trees, etc.

This takes proper Engineering to calibrate the Cell Tower to work as good as it can in Noise.

decibels are absolutely used in Noise Floor Measurements and Tower Top Receive Amplifier Calculations.

Tower Top Receivers also have internal Noise known as the NF = Noise Figure.

And as expected Noises are all additive to some degree as long as there are many simultaneous signals present.

BOSE Noise cancelling Headphones, they analyze the Noise around you and a circuit creates

a 180 Degree Noise signal and they cancel out, leaving you in blissful silence around the screaming kids, of the drone

of the Airliner Engines....

NOW YOU CAN GET A PICTURE OF HOW DECIBELS ARE APPLIED IN RADIO

THERE ARE GAINS AND LOSSES.... PLUS AND MINUS, GOOD AND BAD

RADIO IS PRACTICAL, WE ALL DEPEND ON RADIO SO OUR CELL PHONES CAN WORK!

Now, commit these** three DECIBEL dB rules of
thumb** to your "Membrane"...

It makes You, a Visual Mathematician, not a just a Rapper, a Radio Rapper!

You can Rap about dBm and Signal Levels!

Math will always squash Rap

But Rap seems to always win over Math

As we have less STEM students today

(now how about that, and you sucked at Math...)

Being Cool is about being Smart

Just think about what career you want

Fast Money or Health & Balance?

*I think it is better to Fade Away than to Burn Out (my
opinion)*

THE THREE DECIBEL THING ALL ENGINEERS *
SHOULD* KNOW

#1 NUMBER ONE

+3dB = x2, or twice

then it follows that -3dB is half the amount.

(If I have a 10 Watt Amplifier, if I raise the Gain by 3 dB. I have = 20 Watts)

(If I have 100 watts and lose -3dB = 50 Watts)

#2 NUMBER TWO

+6dB = x4, or four times

then it follows that -6dB is a quarter of the amount.

(If I have a +6dB Antenna and my Transmitter has 3 Watts, I am transmitting = 12 Watts of Power)

(If I have a 50 dBm of Signal at my Antenna, and lose -6dB of Gain, I end up with 44dBm)

#3 NUMBER THREE

+10dB = x10, or ten times

then it follows that -10dB is a tenth of the amount.

You can also talk dB's in a purely relative sense, with little Math.

Ex. A VHF transmitter transmits +20 dB of Power, I lose -8 dB in the Coaxial Cable and the Antenna has +10 dB of Gain

What is the resulting Radiated RF Power in dB?

dB = (+20dB) + (-8dB) + (+10dB) = +22 dB

Math in dB's is simple, you just add and subtract, so how much is 22 dB in Watts?

Good question!

Only if you are given the actual values of what is being measured, can you know the value.

Let's look at the above.... and below...

Lets assume that the **reference power** is 1 Watt of RF Power;

22dB = 10 log (Watts/1)

10^{(22/10)} x 1 = Watts

158.48 Watts = 10^{2.2}

So +22dB referenced to 1 Watt, is 158.48 Watts, radiating from the Antenna, into free space..

So... how many Watts is 20 dB = 10 log (Watts/I) when referenced to 1 Watt?

20 dB = 10 log (Transmitter Watts/1)

(divide both sides of the equation by 10)

20/10 = log (Transmitter Watts/I)

Then take the **"anti-log"** of the **"log" function** to
eliminate it

then raise the left hand side as **Ten** to the power of the
division that equals 2.0

10^{(2)} = Transmitter Power = 100 Watts

Looking at this from the practical sense.

Some RF Engineers just memorize some of the typical dBw values so that just by looking at the value

They know the Watts.

If we all just worked in Watts, it would be so cool, dBm is not as intuitive as Watts

Just like Celsius is not as intuitive as Fahrenheit, its all about perspective.

And perspectives can be changed, you cannot change that weird Cousin, unless you change your perspective on Him.

But without the dB, our lives would be far more computationally tedious, dB makes things visually attainable

though the power of Logarithms.

An example of an RF Radio Transmitter in pure dB's:

*A 100 Watt Transmitter connects to a +10dB Antenna through an -8 dB lossy
coaxial cable*

*a Typical scenario at a frequency of 1.2 GHz*

*dB = 20 dB + 10 dB - 8 dB = 22dB!!! easy as shit...*

*Almost close to Flunking 1st Grade.... or being sent back to
Kindergarten.*

*You see how you knew that a 100 Watt Transmitter was 20 dB?*

Now if I ask you out of the blue, how many Watts can I radiate given a +6dB Antenna?

Your "membrane" will recall that 6dB is 4x (four times)

@ +6dB Gain...

2 Watts = 8 Watts Radiated (ERP is Effective Radiated Power)

63.87 Watts = 255.48 Watts ERP

100 Watts = 400 Watts ERP

278 Watts = 1,112.00 Watts ERP

1000 Watts = 4000 Watts ERP

+6 dB is 4x the Power...... simple, easy, no real Math other than multiplication.

Do you need to be a genius to do RF Engineering, NO!!!!

You just need to get off that Sofa and open a book and read.

Note: RF and Antennas Gains often come in 2 dB values.

dBi and dBd on Spec Sheets... another freaky thing to worry about.

But when you are aware, and have made a few mistakes, you will catch on.

Like getting slapped on the head by that nasty bully each time He walks by.

Until one day, you will Google, how to get back at a Head Slapping Bully.......

Then He will learn a lesson on messing with the Mind, not just the Body.

The formula for this is dBi = 2.15 + dBd

dBi = 2.15 + dBd

This means that a regular Dipole Antenna (reference) is 2.15 dB less than an Isotropic Radiator

that is an ideal point in space that radiates in all directions equally.

This means that a Dipole is not an Isotropic Radiator, it sends RF power unequally in space.

It radiates with 2.15 dB less than the ideal in all directions.

Photoshop, is the way that people look like an Isotropic Radiator in a Magazine

When they are just Dipoles being manipulated to look perfect, and that does not exist.

Where i stand Isotropic and d stands for Dipole.

**Antenna Datasheets have dBd and dBi and you must be careful... **

**use
the right one in your Radio Coverage Software!**

I digress, as this is RF Antenna Engineering, not Audio.

But you can see the applications of the Decibels abound

From your iPhone to your Tinder Hookup

From your Tweet to that Facebook
post

You owe yourself the knowledge of how it works, else smarter people will play you like a Violin.

Street Smarts are critical, but Technology Smarts are also important.

The Decibel extends outward, beyond Audio Amplification, into Radio and also Sound (Acoustics).

You just read through some very cool shit, now I am taking you out of RF and into Audio on your

**Decibel Adventures... to be continued**

**So how does Sound, Live Music, and dB's work out, what is this all about?**

So we can view dB in a relative sense, or when we know the reference

we can calculate the actual Power or Voltages involved.

Curiously marketing companies depend on that the customer, does not know what I am about to tell.

Audio Amplifiers, must be 10x more powerful for You to be able to hear a noticeable difference in Volume.

When you spend money on a 1000 Watt Car Amp, you are really only using 20% of that Power,

The rest of it stays in your Ego and Imagination,

This is how Sound works, and how "Marketing of Watts" is deceptive and deceiving

It empties your wallets faster than a Bad Date....

So what does needing +10 dB more, have to do with my Rattling License Plates!!

Yikes.... and Yes it does... you don't need 1000 Watts to Rattle....

So if I have a 100 Watt Audio Amplifier

I am convinced by an Audio Salesman that a 200 Watt Audio Amplifier will make my world Rock better, will it?

**Let's do the Math;**

dB = 10 log (200/100)

dB = 10 log (2)

dB = +3 dB

Nope, you won't hear a difference, **you need +10dB**

So Yes you get +3 dB more Power, that is twice, confirmed by the formula

And you just emptied $300 from your Savings to buy 100 Watts more for nothing!

Doubling Audio Power with just a +3dB increase goes from 100W to 200W, sounds like a great improvement?

Dude, you need +10 dB more power to hear a difference... (and feel that extra Bass shake your booty).

How about if I spend an extra $500 to get a 300 Watt Amplifier?

Is that much more than your 100 Watt or 200 Watt Amplifier?

**Let's do the Math;**

dB = 10 log (300/100)

dB = 10 log (3)

dB = 10 * .4771

dB = +4.71 (100 Watts to 300 Watts.)

dB = 10 log (300/200)

dB = 10 log (1.5)

dB = 10 * .17609

dB = +1.76 (200 Watts to 300 Watts.)

dB = +1.76 dB or +4.71dB more power, is that worth the extra $800, not.

*I don't think so Dude, save it for that Engagement Ring....*

*Will you hear a big difference, probably not.*

A 200 Watt Amplifier and a 300 Watt Amplifier sound pretty much the same as a 100W Amplifier

They just have more Power Headroom that can be handy with the fidelity of Audio "Transients".

You still need pretty much 10x the Audio Power to perceive a noticeable difference in Power.

So put another way, you really need *1000 Watt amplifier* to have a better
*explosion* than a 100 Watt amplifier.

At 1000 Watts from 100 Watts:

dB = 10 log (1000/100)

dB = 10 log (10)

dB = 10 * 1

dB = 10; you made it!!!

At 1000 Watts from 200 Watts:

dB = 10 log (1000/200)

dB = 10 log (5)

dB = 10 * .6987

dB = 6.98 or 7 dB not quite...

You may hear a slight difference, but not +10dB

Just stay at 200 Watts....

CAR STEREO POWER MADNESS

BUT YOU WANT 1000 WATTS IN YOUR CAR?

IF YOU USED THOSE 1000 WATTS CONTINUOUSLY, YOUR SPEAKER COILS WOULD MELT

IN FACT WITH MOST HIGH POWERED SYSTEMS

THE 1000 WATT AMPLIFIER IS RUNNING BETWEEN 50 & 80 WATTS AT HIGH VOLUME

BUT YOU ARE BARELY ABLE TO SEE THE ROAD DUE TO VIBRATIONS :)

WHEN BLASTING, THE REST OF THE HEADROOM IS JUST FILLING YOUR EGO

KNOWING THAT YOU HAVE 1000 WATTS TO SHOW YOUR FRIENDS

IT MAKES YOU FEEL BETTER, SO THE 1000 WATTS DOES HELP, EMOTIONALLY

You are made to believe in **Thousands of Watt**s, but
Audio Power is not
Linear

Neither is Climate Change, IT IS NOT LINEAR...

But I won't do that now, Climate Change is a touchy subject, but we can see it, if we open our eyes.

500 WATTS

When in fact any Audio Amplifier runs full-out at 20-25% Continuous Power

That Audio Dummy Load, it heats up as it is a Resistor.

Your Speakers are not Resistors, so you cannot power test your amplifier with a Speaker, it would melt the Voice Coil

This a logarithmic thing, the more you want, you need to pay much more, for a difference, much more.

So the next time you enjoy a 10 Watt Tube Amp remember you need a 100 Watt Tube Amp to make a discernible audible difference.

Then you need Power Hungry Speakers to be compatible with your 1000 Watts.

It is just as absurd as raising the Basket if Players are now all 8 ft. tall, you need bigger more powerful speakers.

Like that Ferrari in a 35mph Speed Trap Town....

I note that speaker efficiency is cast aside, as this obviously was not discussed here.

What you are paying for when you but a 2000 Watt Car Stereo is probably just 100 Watts of Music Energy, and 1900 Watts of EGO.

If you ever could run the system at 2000 Watts, you would need Speaker Voice Coils the size of a Garbage Can.

You my friends, are victims of the **More Watts Marketing** that has been
around for Decades.

You lay out Cash, and then use 10-20% of what you purchased on a good day at the Park.

Do you see the Marketing Watts and Power *Hype Fog* start to lift?

The reality of Audio Amplifiers, all you really need to Rock out is 100 Watts.

More than that, you have to get a Class D 1000 Watt amplifier, cheaper than Class A/B.

Audio amplifiers use the **HEADROOM** to not distort when cranked up.

So
the reality here, that extra power you pay for is really a guarantee that
when you crank up the Volume

You will not distort until you go deaf.

This is how our ears work with relation to Sound, and Sound Power, SPL = Sound Pressure Level.

Also dB, is a dimensionless unit, unless you know the reference and above are the typical types of things the dB is used for.

So, you can in fact work with dB and have no clue what the F it is about (Power, Voltage, Radio, Sound)

You must be informed after or before the fact what it was about, else this is exactly how teachers teach Math

they don't often give real fu!@#ing examples
of why you take the **Sine** or **Cosine** of an Angle??

What is Tangent? How do I use it in my Career?

**TRIGONOMETRY **

Cos, Sin, Tan & Friends...

Sadly, some Math teachers don't really apply the Math, they just teach it.

Until a Court Case asks them, to Calculate the Force of Impact on a Pedestrian hit by a Car

that my friends is applied Math.. not Partial Differential Equations, but that's what they call them

**ALL MATH IS APPLIED MATH**

$1 Dollar in account + $1200 Dollars deposit = $1201 Dollars Balance; you just deposited $1200 in your Bank Account

You applied Math.... (cool stuff Man).

Just one look above and You may see something *familiar* if you are
into Electronics, the Functions of the Waves....

Trigonometry is awesome, but most Math teachers suck at teaching it!

Now, if they would take an *Oscilloscope* and a *Signal Generator* to class

and show you how to determine the Frequency of the Waveform below wouldn't that be cool!

THE OSCILLOSCOPE - THE MOST USEFUL AUDIO TOOL, AFTER THE VOLTMETER (VOM)

*THE OCILLOSCOPE ALLOWS YOU TO SEE INSIDE OF THE PATIENT (YOUR
AMPLIFIER)*

*IT'S LIKE THE MRI OF TUBE AMPS, YOU CAN LOOK AT THE MUSIC, NOT JUST
THE POWER*

*SUPPLY VOLTAGES WITH YOUR METER (BUT JUST AS IMPORTANT)*

Below I took this picture of my Oscilloscope of a Sine Wave, so how do I know the frequency?

Just by looking at this picture I can determine the frequency?

**Yes you can, I will show you how...**

Notice that we see what is called a Sine Wave (Sinusoidal for M.I.T. and Georgia Tech Graduates)

**OSCILLOSCOPE TRACE OF A SINE WAVE**

Each TIME division on the X axis is 0.200 ms (or 0.002 Seconds) from the display T = 0.2ms

The Vertical Y Scale is 0.1 Volts per division so by inspection, that Sine Wave is 0.5 Volts Peak to Peak.

Amplitude is easy, you just count the vertical divisions from the Sine Wave Max and Min...

You can see that it crosses 4 complete horizontal lines, plus 1/2 of a top and 1/2 bottom, that is 4 + 0.5 + 0.5 = 5 divisions

The value of each division, from the display, is 0.1v, hence 0.1v x 5 = 0.5 Volts (peak-to-peak).

The RMS (Root Mean Square) value of that Sine Wave is .7071 of the Peak to Peak

So that Sine Wave is RMS = 0.5 x .7071 = 0.3535 Volts AC RMS

If you apply Ohms Law you need to convert AC Peak to Peak to RMS, so that the calculation works.

If I was to measure this across a 100 Ohm Resistor, the Power dissipated
would be P = V (RMS)^{2}/R

P = 0.3535^{2}/100 = 0.00125 Watts = 1.25 Milliwatts so a 1/8 Watt
resistor would not work, you need a 1/4 Watter.

You can see how much information that simple Oscilloscope Picture offers the "knowing Tube Amp lover"

You can do it, I know you can as you have read down to this point.

I am here to help, just shoot me an e-mail, I love to clone my type, and you will

be a much better Tube Amp owner and loving restorer once you get

my same Infection, this is not COVID 19, this is "TUBUS MAXIMUS 22"

HOW ABOUT THE * FREAKIN* FREQUENCY...

YOU ARE ON A TANGENT DUDE!

For the Frequency of the Waveform you look at the 0.2 ms, that is a measure of time

You need to convert that milliseconds of time into seconds of time by moving the decimal point

When you do formulas everything has to be in the same units.

In the Metric System we use MKS - Meters, Kilograms and Seconds.

In electricity it is VOLTS, AMPERES, OHMS, FARADS, HENRY'S and WATTS

As long as you place every number in the same unit base, you are awesomely getting ahead!

So to go from milliseconds to seconds, just move the decimal point 3 positions to the left

You then convert to 0.2ms to 0.0002 Seconds, roll the decimal 3 positions to the left

1,2 and 3 to the left, so easy dude, too easy.

Remember that when we take a small number such as 0.2ms and want to convert that to Seconds

Seconds is a much larger unit than milliseconds, so the number in seconds
will be a small one....

0.2ms = 0.0002 seconds..... the decimal went to
the Left.

If you took 0.0002 Seconds to Milliseconds, that decimal point would move three positions to the right..

0.0002 seconds = 0.2 ms

How about Microseconds, that is an extra 3 positions of the decimal point to the right..

0.0002 seconds = 0.2 ms = 200 nanoseconds and so on...., another three positions to the right are picoseconds

200 nanoseconds = 200,000 picoseconds

Engineering notation is always about moving the decimal point 3 positions left or right, easy as pie.

0.2 milliseconds is 0.0002 Seconds, as a millisecond is 1/1000 of a second, a smaller amount of time

*The blink of a Human Eye takes 1/3 second or 333 Milliseconds, or on
the Oscilloscope a Sine Wave of that Period*

*would have a frequency of:*

*f = 1/T = 1/.333s = 3 Hz*

*That is a low frequency indeed, much lower than the 20 Hz... *

*Now, from start to finish, in the Oscilloscope picture, the Sine Wave Time
on the X Axis starts and stops in 1 cycle*

You can see this across 5 vertical divisions

We are not interested in the Y axis as than is Amplitude (we already went there), but we use the Y axis lines to measure across the X axis.

So the equation for frequency is;

**Frequency = 1/(Time or Period of Time) or f=1/Time, f=1/t**

I have 5 vertical divisions of 0.200 Milliseconds, this is 5 x .0002 Seconds = 0.001 Seconds

So the Frequency of that Sine Wave is:

**frequency = (1/0.001) = 1000 Hertz = 1000 Hz**

You just learned how to, by just looking at a Scope Display determine;

**#1: **The Amplitude of the Sine Wave by inspection
only

**#2: **The Peak to Peak Voltage of the Sine Wave by
inspection and some Math

**#3:** Frequency of the Sine Wave by inspection and also Math

**#4: **The RMS AC Voltage Value of the Sine Wave by Googling
RMS for the conversion constant .7071

Are you still scared of looking at an Oscilloscope trace, Nah, you got it now!

**POWER TESTING YOUR TUBE AMPLIFIER**

Oscilloscope, Audio Signal Generator, Audio Dummy Load & AC RMS Voltmeter

Adapters, Cables, Calculator, Pencil & Paper

How many Watts? do you really want to know.

The question everyone asks You when you tell them You own an Amplifier,
**how many Watts?**

The cool part, is that when you connect your Tube Amp to a Audio Dummy Load and use the Oscilloscope

to look at the Sine Wave produced, when you connect your iPhone Signal Generator app to the Amp input.

The answer to this question becomes visible and measurable.

Sine Wave Amplifier Power Testing, allows you to determine and see how many Watts your amplifier can produce.

You have just created an Amplifier **Lie Detector**!

You crank up the Volume, until that Sine Wave display Distorts

then back off the Volume (Signal Level) until it looks clean again.

With your **True RMS Digital Voltmeter **now** **measure the **AC RMS Voltage
of that clean Sine Wave**

As your Tube Amp is heating up the 100 Watt Audio Dummy load you purchased from "Parts Express"

Friends, that is how you power test your Tube (or Solid State) amp. Quickly, no hassles.

You run the Amp(s) into an Audio Dummy Load(s) and bridge that connection into your Oscilloscope while your AC RMS Digital Meter

brides the + and -, provides you the AC RMS Voltage your Amp develops across that 8 Ohm Power Resistor on your AC Voltmeter Display

JUST "KRANK" IT UP TO MAX CLEAN SINE WAVE

JUST UNTIL THE WAVE STOPS LOOKING CLEAN

NO DIRT, IT NEEDS TO LOOK LIKE THE TRACE

ON THE OSCILLOSCOPE ABOVE......

NICE AND SQUEAKY CLEAN

THIS A VISUAL THING, VERY COOL, NO MATH!

HOW TO DO OHMS LAW, THE RIGHT WAY

Once you wrote down the AC RMS Voltage use Ohms Law, to calculate the Watts of Power.

Power =
Watts = V^{2}/R

If your meter read 12.4 Volts AC RMS @ 1000 Hz

Power =
Watts = (12.4)^{2}/ 8 Ohms (Dummy Load Resistance)

**Power = Watts = 19.22 Watts**

Rounding up you have a 20 Watt Tube Amplifier at 1000 Hz

Now, you repeat the same measurement at 20Hz, 100Hz, 500Hz, 5000Hz, 10000Hz, 15000Hz, 18000Hz

Repeat each measurement and You have just Power and Frequency tested your Tube Amp.

If you have a Stereo Amp you will need a separate Audio Dummy Load for each Channel.

On your Dual-Trace Oscilloscope you can view both Channels Simultaneously.

This is also a great way to look for Channel to Channel Power Balance (or lack of).

You will likely get less Power when you go down to 100 Hz & greater Powers above 1,000 Hz

What you will find is a POWER CURVE if you take enough data points to plot the results in MS EXCEL.

each extreme will roll off in Power, that is perfectly normal for a Classic Tube Amplifier

REMEMBER TO KEEP THE SINE WAVE CLEAN ON YOUR OSCILLOSCOPE DISPLAY

NO SUCIO, NO DIRTY SINES, NO CHEATING, NO CLIPPING

**MR.CLEAN**

**SO DOES MATH RULE OR WHAT!**

Hey Sine, Cosine.... Log, Pi, get the picture? Trigonometry? Music? Amplifiers?

If you know Trig it helps to understand Amplifier Power and much more about the world

You would not
have been getting *Stoned before Trig Class*!

We need more "Patch Adams" Math teachers, and less of what Roger Waters sang about on

**THE WALL**

We need Teachers that make Us laugh at the Formulas, not hate them.

ABOUT SOUND POWER - SOUND PRESSURE LEVELS (SPL)

Sound as in a Concert, at Home or a Political Rally Megaphone is dB-SPL

Sound is expressed in SPL (Sound Pressure Level) as in dB-SPL

the denominator (reference) is 0.00002 Pascal

V_{2} = 0.00002 Pa (Pascal) a unit of Pressure.

So when you are told that Hearing Damage happens at high SPL, you may not have known that

Deep Purple was the highest measured Rock Concert in History +117 dB !!!!!

*In 1972, Deep Purple was recognized by the Guiness Book of World Records*

* as the "globe's loudest band" for a concert at the London Rainbow
Theater *

*during which three members of the audience fell unconscious.*

+117 dB Deep Purple SPL, how much sound pressure is that, and how far from Stage?

Well the SPL is based on the distance form the Sound Source

Sound decay's over distance, the farther from the Band, the lower the SPL

a simple dB SPL formula does not take into account distance.

So I have to guestimate this from the +117 dB.

Let's assume that the measurement was not taken on-stage (most likely)

but at some distance away from the Stage to make 3 people pass out.

I opened an online SPL Calculator and ran some numbers on this Concert and this is what I got;

Let's say that someone measured +117 dB SPL standing 40 feet from the stage

This sounds reasonable for a good spot up front close to Blackmore, Glover, Paice, Lord & Gillan

At 40 feet, and +117dB, the Band must have been playing near 133 dB SPL!!!

How these guys survived, is amazing, they certainly had Hearing protection.

Ted Nugent almost went deaf on Stage

Ted knows the Hazards of being a Rock Star on-stage with no hearing protection.

+117dB is an "insane" level of Sound Pressure Power @ 40 feet from Stage.

**Sound is measured in decibels (dB). **

**A whisper is about +30 dB**

**Normal conversation is about +60 dB**

**Motorcycle engine running is about +95 dB **

**Noise above +70 dB over a prolonged period of time, may start to damage your
hearing. **

**Loud noise**** ****above
+120 dB
CAN CAUSE IMMEDIATE HARM****
TO YOUR HEARING**

SounSound pressure level (SPL) is the pressure level of a sound, measured in decibels (dB)

Sound is equal to 20 x the Log_{10} of
the ratio of the Root Mean Square (RMS) of sound pressure.

the reference sound pressure in air is 2 x 10-5 N/m2, or 0.00002 Pascal

This is the reference value in the denominator of your SPL = 20 log (Pressure/0.00002)

*Recognize the Formula? same one, but a different application, Audio
Sound Pressure!*

So people, when you **Crank up your Audio System**, try to keep the
**SPL** below
**85dB MAXIMUM**

Keep your distance from the Speakers..... if the system is loud.

Buy a Sound Level Meter, cheap insurance I have one and it works great to save what is left of my Hearing

Measure the average SPL from your Sofa, and adjust volume to suit You (and keep the Wife happy)

*I lost hearing at Van Halen in 1991, Roanoke VA.*

My ears rang for 4 days, after the show, and all the way Home from the Show

I was 50 feet from the stage, and had to get away after the 4th song was over

My wife and I leaned across the rear wall, it was LOUD

During Alex's Drum Solo, a panel of the Central Scoreboard came off and

fell down, cutting a Lady who was rushed to the ER by Security

Covered by a bloody White Towel!

If you were at that concert, you were lucky.

Not to be under the Scoreboard that was more than 60-70 ft. above the arena

Not even RAMMSTEIN at the Globen in Stockholm was as loud

And Hearing Protection was being provided for FREE at that Show

You got to Love the Swedes, they have a Wonderful City and Great People

I just wish that the new entrants, would respect that, and not behave so entitled

St. Maarten decibels & thrills

Radio Signals like Sound attenuate over Distance

This is why you need Hearing protection when close to a 747 Plane

Believe me, I was there in St. Maarten having a Beer near the Runway

and it is LOUD. These people below are nuts!

Those Engines can kick up rocks and take out your Eye!

They hang on to the Fence and challenge Darwin, not I.

**Now how about Current?**

*Currents are not usually expressed in decibels..... just a fact of the
matter, I will do some research as to why?*

*Also just as well it is unusual to find electrical specs in terms of AC or DC Currents
and it has always bugged the F. out of me as an Electrical Engineer*

*I always shout: GIVE ME THE FKIN CURRENT DRAW!* DAMMIT!

JUST ASSUME A POWER FACTOR OF 0.9 IF AC, MAKE A DAM ASSUMPTION!

*Without knowing the Current loads, it is more difficult to do a solid Power Load
Analysis!!!*

*And if they just give me the load in Watts, if it is DC great, but in
AC I need the Power Factor!!!!*

*When you see a decibel, it must have some basis.... *

*else you will not
be able to do Apples to Apples comparisons...*

*If you just get dB's you are forced to exist in the world of Addition
and Subtraction of dB's and*

*that is cool sometimes, and very un-cool in other situations.*

*The beauty of the decibel is that they add and subtract as whole
numbers....*

*The reality of Engineering, we also have our Pet Peeves.*

Commonly used Decibel notations

dBm (referenced to 1 milliwatt)

dBw (referenced to 1 watt)

dBuW (referenced to 1 microwatt)

dBv (referenced to 1 volt)

dBmV (referenced to 1 millivolt)

dBuV (referenced to 1 microvolt)

there are more, just Google them....

http://www.sengpielaudio.com/calculator-db.htm

You must learn Ohms Law, end of story

No Ohm's Law, No practical Amplifier Repair verification

No Joy without measurements!

Working "blind" is not a good place to be

Faith is for religious folks

Science relies on hard data

Politics relies on backstabbing

Herr Georg Ohm

VOLTAGE = V

CURRENT = I

RESISTANCE = is futile :)

WATTS = POWER = P

Voltage in Volts = Current x Resistance is Linear

V = I x R

I = V/R

R = V/I

Power in Watts is Linear and also Exponential

Watts = P = V x I

Watts = P = I^{2} x R

Watts = P = V^{2}/R

Hello again, its your Membrane...

Memorize these formulas, you will not regret them one bit

The troubleshooters "Secret Sauce"

Like they were your Girlfriends/Boyfriends/Partner/Dealer's new Cell Phone #

The great thing about Electrical Circuits, they all follow Laws...

Kirchhoff's Law, Norton's Law, *even Harvard Law*.....

*Unlike some, who may eventually do something stupid and....*

Congratulations if you have made it this far..., You are on the path towards Tube Valhalla

The righteousness of the Electron Tube, Music in a Vacuum, just like Astronauts in Space

The electron jumps from the Cathode to the Plate

The Astronaut jumps from the Earth to the Moon.

Both travel in a Vacuum.

Dude, that was sooo deep!

TUBE VALHALLA

*Not currently broadcast on Mainstream Media, or Streamed on YouTUBE*

This is the place that you have been working towards

Tube Valhalla.... enjoy my Web Pages, you just graduated

"Summa Cum Valvo"

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