A precise analysis of an L-network for impedance matching below 3 MHz. The desire for “an ideal” characterization of the circuit parameter space for utility in fabrication by hand. The reduction to a pure mathematics problem.

Introduction

This is a full description of a situation often encountered by scientists in the process of fabrication of the NMR probe. The analysis requires some tedious complex algebra, a bit of circuit theory, and enforces a matching condition. I tried to write this so that one may infer the cirucit theory from context. If there is a problem, just ask.

We will examine the impedance of this reactive L network

Goals of this challenege:

Characterize the parameter space of the variables Cm, Ct, ω, L, r and produce some useful set of tables for lab, in which the relationship between Cm and Ct is known for a given ω L and r. Furthermore to ponder the level of greed allowed. Which parameters limit others? Compare this with what the laboratory reality is.

——

One must always strive for impedance matching conditions to be satisfied, which for us means 50 ohms real. So we must

enforce

Im_Z = 0

Re_Z = R := 50 ohms

—–

These requirements are nasty if you allow the impedance of the coil to have a small (but very physical and influential) real part r

Z_coil = j ω L + r

So the total impedance is

Z_tot = -j / (Cm ω) + Z_coil || Z_Ct = Re_Z + j Im_Z = R + j 0 = 50

Note:

* Z_m is the impedance of the matching cap only
* Z_t is the impedance of the tuning cap only
* the notation A || B means “A parallel B” and A || B = ( 1/A + 1/B)^(-1)

Since Z_coil has a real and an imaginary part, the expression for total impedance is a headache.

So I did it by hand, and with mathematica, and iteratively found what I consider decently short code with reasonably concise expressions. Here we go.

 

—–

Clone the mathematica stuff here

 


git clone https://github.com/Altoidnerd/NMR-Tank-Circuits

 

In which there is a file where I do in fact show the real and imaginary parts of Z_tot are:

real part (which we denote Re_Z…please note the sloppyness. Here w is ω)

Re_Z = r/((r^2 +
L^2 w^2) (r^2/(r^2 +
L^2 w^2)^2 + (T w - (L w)/(r^2 + L^2 w^2))^2))

and imaginary part (Im_Z)


ImZ = (-(1/(M w)) - (T w)/(r^2/(r^2 +
L^2 w^2)^2 + (T w - (L w)/(r^2 +
L^2 w^2))^2) + (L w)/((r^2 +
L^2 w^2) (r^2/(r^2 +
L^2 w^2)^2 + (T w - (L w)/(r^2 + L^2 w^2))^2)))

where we eliminated the need for subscripts but denoting Cm := M and Ct := T.

How do we make useful data from these equations? To answer this, we must first assess what the experimenter can really control.

* coils are hard to wind and have prescibed results. In general, the parameter r is less than 1 ohm, but its actual value is not constant through frequency sadly. It must be treated as such.

* A typical coil inductance L satisfied 1.0 uH < L 30 uH. Intermediate values such as 8 uH tend to be the most difficult to fabricate. A coil inductance of 8uH I find would be useful for lower frequencies, below 3MHz, which are currently causing me problems. It is here the equations become extremely sensitive.

* The capacitance T and M can within reason, be expected to continuously vary between 0 < T,M < 1 nF and even more reasonably if the upper boundary is around 300 pF.

* the frequency is going to satisfy 1 MHz < f < 30 MHz; so ω = 6.28 f so we can say about, that
1 e7 < ω < 3e8

I have made many charts. Got any brilliant ideas?

——–

A typical annoying situation in lab would be:

Drat. To reach the target frequency, we must either replace the capacitors with larger ones,
or exchange the coil with one of larger inductance. Which will take me less time?

I usually do not know in fact. I either make a intuitive guess, prepare some primitive tests, or try a bit of each.

The code in the github repo above will give you some parameter sliders. You can try plotting M, and T vs ω as L and that little tiny r are varied…I still must get to the bottom of these matters, such as, the qualitative effect of increasing r at fixed ω and L etc. How to encapsulate all such desirable relations in a single concise set of diagrams is what I truly seek, from the kind theorists of who may read this.

——-

Final thoughts.

I have studied this problem up down left right…I wrote some interesting special cases down here, but I believe there is more to be known about these equations that could be of service to the designer.

Posted in Electronics and Engineering, Physics and Mathematics, Stuff

Sad grep I – V


~$ sad grep poetry of the internet


I

# facebook | grep brains

#

 

 

II

# cat ./telecom| egrep (options|competit.?.?.?.?.?)

#

# dmesg

comcast

#

 

 

III

~$ ls

~$

~$ pwd

home/fridge/

~$ ls -laR | grep food

~$

 

 

IV

# cat ./reddit/r/bitcoin/* | grep criminals

Display all 169,236 possibilities? (y or n)


 

 

V

~$ ./github/ | grep working code

OSX

~$

 

 

 

 

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Posted in Bitcoin, Electronics and Engineering, scamcoins, Stuff

When should I sell my Bitcoin Mining hardware? Bitcoin Mining Hardware Resale Value vs Projected Return

Altoidnerd:

It’s interesting to look back at these “old” numbers from November 2013!

20140605-062924.jpg

Originally posted on altoidnerd science:

If you have any questions about this process, you can contact me with the form below!  Happy mining. 

In general, the profit margin for miners becomes slimmer through time as the competition to break into bitcoin mining increases and the barriers to entry are higher than ever.  Customers have in general had poor experiences with ASIC manufacturers who have delivered the mining products late, making the hardware purchase a net loss for the investor.  The situation is not so grim for the miner, however, because the bitcoin price and price velocity are as high as they have ever been, and are not showing signs of flinching.

Despite the apparent victory for the miner when the price rises, it is a common misconception that a positive return of investment can be saved for a poor mining hardware purchase if the bitcoin price rises enough.  This is not actually true – well…

View original 1,579 more words

Posted in Bitcoin, Physics and Mathematics, Stuff

Does a single electron moving at constant velocity generate electromagnetic waves?

H150_mmmm_evt1_persp1

Nope.

Redditor /u/Mimshot gave the following example:

If an observer is near the path of a small, moving charged particle (unless there’s some special quantum effect I’d love you to tell me about if it exists) the observer will see the E field increase and then decrease and will see the B field ramp from baseline, then reverse direction, which is certainly wave-like. I’m not saying it radiates photons, but I’m wondering if “no, it must be accelerating” is a complete answer.

Is there some quantum effect I’m missing?

 

Image

I “know” immediately there is no radiation in this case, because the theory of relativity tells us we can use a frame of reference in which the particle is stationary. Hence, as a rule, only accelerating particles radiate and thus give rise to traveling waves. Nevertheless, this question did get me to think about what the fields would be like in such a situation. A passing electron would seem to have some time dependent magnetic fields because the “ramp” explanation above, but it cannot be the case since we should know, just “because”, only accelerating charges radiate.

After some thought I came up with the following proof that the magnetic field is static in this case.

Start here

J(r,t) = ρ(r,t)v(r,t) = e δ(r – r’,t)v(r – r’)

v has no time dependence.

The current I is ∫ J d2 x’

I = ∫ d2 x’ e δ(r – r’,t)v(r – r’) = e v = a constant

To find B we use ampere’s law for some closed loop

∫ B dx = μ I = constant

If you’re concerned about the ∂E/∂t term lets look at the full maxwell equation

 x B = μ J + μ ε ∂E/∂t

Applying the operation ∫ d2 x to both sides gives

∫ B dx = μ I + μ ε ∂/∂t ( ∫ d2 x E )

The RHS of the above equation is simpified using gauss law, the integral gives the charge enclosed by a surface

∫ d2 x E = q/ε

so

∫ B dx = μ I + μ ε ∂/∂t ( q/ε )

but ∂/∂t ( q ) = 0

so that term doesn’t change things.

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Posted in Electronics and Engineering, Physics and Mathematics, Stuff

Generating arbitrary sounds from pure functions – mathematica virtual synthesizer

image

An “organized” source is being built here -

Help out:

https://github.com/Altoidnerd/Mathematica-Synth

 

A picture says a thousand words…so here is the tarball of code fragments:

http://www.phys.ufl.edu/~majewski/Mathematica-Synth.tar.gz

4b1e206b50f68dfa0fb464eb0d06116c Mathematica-Synth.tar.gz

image

Video example:

https://www.youtube.com/watch?v=CUSGOjjfURc

 

 

 

 

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Posted in Electronics and Engineering, Music, Physics and Mathematics, Stuff

Technical Analysis

Originally posted on Crypto Frenzy:

Lately, I have built up my skills in Technical Analysis. I learned about moving averages, accumulation indicators, and more.

View original 357 more words

Posted in Bitcoin, Stuff

Theorem for impedance matching in NMR tanks using L-networks facilitating broadband frequency sweeps for unknown quadrupolar resonances in solids.

Wz02hah

 

Locating pure NQR spectra precisely would in many cases clarify NMR studies.  Furthermore NQR is indicative of internal field geometry in solids and is thus useful in the identification of quantum phase transitions.

The pursuit of pure NQR is difficult however because the resonant frequency is sample specific and is often unknown. Unlike in the case of NMR, the frequency cannot be controlled in the laboratory, but is rather a property of a material that is a fingerprint of the local environment of the nucleus in question.  

In general, operating a pulsed spectrometer at various frequencies requires the corresponding adjustment of the two capacitors shown below. Reducing the parameter space to a single value would make sweeping much more efficient. Any shortcuts  and tricks to allow easy sweeping could greatly accelerate understanding of NQR in yet unstudied samples.  

This general probe topology is common in the practice of nuclear resonance.

img42

The inductive load is tuned and matched to the characteristic impedance of a transmission line Z0 (usually 50 ohms) by the two variable capacitors C1 and C2. 


Postulate: If the series losses in the coil are set to

R = Z0 / 4, 

then 

C_1 =~ C_2

regardless of the value of Z0, and for any reasonable and f where f is frequency of operation and > 500 KHz. For < 500 KHz the approximation begins to break down for feasible values of L.

Suppose we can utilize transmission line transformers to reduce the effective Zo from 50 ohms to something lower, allowing a higher Q.

If for example the effective characteristic impedance of the tank Z0 = 20 ohms, then one could set r = 5 ohms externally. This results in nice agreement for the caps with L = 30 uH down to around 1 MHz. This would be excellent for sweeping and snooping for unknown quadrupolar resonances in this band, as 14N NQR often appears below 5 MHz.

 

Source tree on Github

https://github.com/Altoidnerd/NMR-Tank-Circuits

Raw copy pasta for mathematica 

https://raw.githubusercontent.com/Altoidnerd/NMR-Tank-Circuits/master/L_network_parallel_resonance_main.nb

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Posted in Electronics and Engineering, Physics and Mathematics, Stuff

Avoid the 5 Common Mistakes of Altcoin Traders

Originally posted on Crypto Frenzy:

Most people new to altcoin trading make similar mistakes. I wonder if it is even possible to avoid them. Maybe they are a necessary learning step.

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Altcoin cryptocurrency trading strategy based on market capitalization distributuion

LINBE

I grab the data from coinmarketcap.com and look at plots of the logarithm of the vector of market caps. It looks kinda like this.

TANH
http://i.imgur.com/TFwe5lD.png [1]

Then I zoom in on sections and look for deviation from linearity, kinda like this.

LINBE
http://i.imgur.com/w8wWnKb.png [2]

I believe the distribution in the first pic (with log scale) to be the inverse hyperbolic tangent

http://mathworld.wolfram.com/InverseHyperbolicTangent.html[3]

Anyway I look for points that are low and buy them hoping their BTC price rises. Gambling yes, but at least it’s math.

Discussion on reddit:

http://www.reddit.com/r/BitcoinMarkets/comments/20j78z/altcoin_trading_strategy_based_on_market_cap/

ALTOIDNERD 2014

Donations: 17NA1jYg5u6ejboArdM7HW4MwSa6cWfnEd

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Posted in Bitcoin, Electronics and Engineering, Physics and Mathematics, Stuff

Bitcoin Resources – market data, blockchain statistics, how to buy/sell/convert bitcoin, news, and forums for bitcoin information

3/15/2014

#######################
Bitcoin resources
#######################

Get started:

https://bitcoin.org/en/

https://www.weusecoins.com/en/

Wiki:

https://en.bitcoin.it/wiki/Main_Page

Market data:

http://bitcoinwisdom.com/

https://coinmarketcap.com/mineable.html

http://bitcoincharts.com/

http://www.cryptocoincharts.info/

Blockchain statistics:

http://blockchain.info/

http://blockexplorer.com/

http://blockr.io/

Original forum:

https://bitcointalk.org/

My favorite crypto-crypto exchanges:

https://www.cryptsy.com/

https://btc-e.com/

Buy/sell bitcoin with USD:

https://coinbase.com/

https://localbitcoins.com/

Subreddits:

www.reddit.com/r/bitcoin

www.reddit.com/r/cryptomarkets

www.reddit.com/r/dogecoin

www.reddit.com/r/litecoin

www.reddit.com/r/primecoin

www.reddit.com/r/peercoin

ALTOIDNERD 2014

donations: 13xdMqkaVKkHKT3ZZx5ikAvQUEkzqpDkDb

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Posted in Bitcoin, Stuff
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