# opeNMR

## preamp

Posted in uncategorized by sfackley on the July 8th, 2008

The board has been milled for a while, but some of the parts just came in today. I can get started building tomorrow!

## frequency synthesizer board stuffed!

Posted in progress-reports by Alec on the July 6th, 2008

Even better, it makes waves (pictures forthcoming). I'll work on characterizing it tomorrow. And if it's solid, make a case and we'll move on.

Still lagging on the meep simulation, though. Been busy.

## meep and frequency synthesizer under way!

Posted in progress-reports by Alec on the July 2nd, 2008

A couple, quick notes: I finally milled the board for the frequency synthesizer. Delaying ordering parts means that they won't be here 'til Friday. Testing and characterization will happen over the weekend.

Also, MEEP's debut has been delayed by a professor's honeymoon; however, the lead developer sent me the source code, and we're up and running. Playing around with it now; hopefully, we'll have some simulations run by the weekend's end.

## rf power necessary for a 20 microsecond 90 degree pulse with a 20 megahertz probe

Posted in miscellany by sfackley on the June 30th, 2008

David Cory asked us to calculate/measure this, so here goes. I assume this is to determine what kind of amplifier we'll need.

We want a 90 degree = $\pi/2$ pulse that lasts $20 \mu s$. So,

$\omega_1 t = \pi/2$,

where $\omega_1$ is the frequency at which the spin rotates when the weak magnetic field, $B_1$, is applied. Plugging in for $t$ gives $\omega=78.5kHz$. Therefore, $B_1$ is given by

$B_1=\omega_1/\gamma$.

Plugging in $\omega_1$ and $\gamma$ gives a weak magnetic field of $18.4$ Gauss.

The magnetic field produced by the coil is related to the current by the following:

$B_1 = \frac{\mu_0 N I}{h}$,

where $\mu_0=4 \pi \times 10^{-7} N/A^2$, $N=10$ is the number of turns, $I$ is the current, and $h=2cm$ is the length of the coil. Plugging in $B_1$ and solving for $I$ gives $I = 2.93 A$.

An NMR probe circuit looks something like the following1 :

Where $L$ is the inductance of the coil, $R$ is the resistance of the coil, $C_T$ is the capacitance of a tuning capactor, and $C_m$ is the capacitance of the impedance matching capacitor. The frequency to which the probe is tuned, $\omega$, is given by the following:

$\omega^2 = \frac{1}{L(C_T + C_m)}$.

At $\omega$, the impedance of the input is given by

$Z_0 = \frac{R(C_T+C_m)}{C_m(1+i R \omega C_T -\omega^2 L C_T)}\approx \left(1 + \frac{C_T}{C_m}\right)^2 R$.

The input of the probe must be impedance matched; therefore, $Z_0 = 50 \Omega$. Also, if we assume we have a coil with length 2 cm and diameter 1 cm, we can calculate the inductance of the coil to be $0.402 \mu H$.  Also, if we assume the quality factor, $Q$ of the inductor is about 100, R is given by $\frac{2 \pi \omega L}{Q} = 0.5 \Omega$. With this information, we can solve for $C_T$ and $C_m$. $C_T = 5.6 nF$ and $C_m=0.6nF$.

Now, we have a signal coming through the input. Let $I$ be the input current, $I_1$ be the current through the inductor, and $I_2$ be the current through $C_T$. We know that $I=I_1 + I_2$ and $I_1 Z_1 = I_2 Z_2$, where $Z_1 = i \omega L +R$ and $Z_2 = 1/i \omega C_T$. If we let $I_1 = 2.93 e^{i \omega t} A$, the we can solve for $I_2$, which is given by:

$I_2 = 2.93 e^{i \omega t} (8.04 \Omega \times i + 0.5)\times 0.112 \Omega^{-1} \times i$.

Therefore, $I = 2.93 e^{i \omega t} (0.1 + 0.056 i)$.

The real input current is given by $0.336 \cos (\omega t + \phi)$ where $\phi$ is some phase. Therefore, the peak to peak voltage [Volts] is given by

$V_{pp} =0.336 A \times 50 \Omega = 16.8$, which corresponds to a power of $28.5dBm$.

Not all of our estimated values are precisely correct; for the setup we were using a $43 dBm$ pulse needed to be 25$\mu s$ long to maximize the signal.

1. http://web.mit.edu/8.13/www/JLExperiments/JLExp12.pdf []

## low noise amplifier chip found!

Posted in progress-reports by sfackley on the June 23rd, 2008

I found an amplifier chip that both has a low noise figure and is affordable. It's made by Infineon and the part number is BGA614. The data sheet doesn't give noise figures below 50 MHz, but the noise figure appears to decrease with decreased frequency. The noise figure of this chip is about 1.8 dB at 50 MHz, as opposed to 2.1 dB at 50 MHz for the lowest noise Minicircuits model (GALI-39+). The only apparent drawback is that the gain is a bit low--only about 20 dB instead of a desired 30 dB.

With all of these amplifier chips, the cooler the chip is, the lower the noise figure. We might try to use a peltier module to get the noise figure down even more. The BGA614's noise figure decreases to about 1.55 dB at -20 C and 50 MHz. The peltier modules sold at minicircuits can produce a temperature differential of up to 66 degrees. So, it seems like cooling might actually be a viable option.

## meep simulation delayed a few days

Posted in minutiae by Alec on the June 17th, 2008

So, it turns out that we'll be waiting to simulate our various magnet arrangements (in particular, with an eye toward answering questions about the feasibility and robustness of stacking magnets) until Friday, at the latest. MEEP1 does not currently support magnet sources. Conveniently, Ardavan Oskooi, the lead developer of MEEP, told me that a new version would be coming out by the end of this week that will simulate what we need. So, I think we'll wait, and if there's no news by Friday, go ahead in MATLAB.

1. MIT Electromagnetic Equation Propagation []

## the “openmr.mit.edu” URL finally works!

Posted in sysadmin by Alec on the June 17th, 2008

## social bookmarking with del.icio.us and Connotea

Posted in sysadmin by Alec on the June 17th, 2008

And a sidenote: we're tagging sites and pages we find useful with the tag openmr on del.icio.us. Feel free to add pages you find to the pool by tagging them with "openmr."

We're also going to be tagging useful papers and publications with the tag "openmr" using Connotea. It's unclear to me whether it makes more sense to just stick to delicious, or to take advantage of Connotea's aim as a reference manager. In either case, we'll also be posting a BibTeX file periodically with references for the purposes of encouraging citations.

## opeNMR on scribd

Posted in sysadmin by Alec on the June 17th, 2008

We've set up an opeNMR group on the document sharing site scribd where we'll be posting the useful documents and articles we (and in the future, others) find pertaining to the opeNMR project.

Feel free to sign up or ask us for an invitation and upload documents you find helpful.

## wordpress LaTeX plugin

Posted in sysadmin by Alec on the June 17th, 2008

So, I've installed Zhiqiang's LaTeX plugin for Wordpress, which you can use to embed $\LaTeX$ into a post by encasing the $\LaTeX$ code in double dollar signs, like so: $$\omega$$, which renders as $\omega$. If you want to center an expression in math mode, simply add an exclamation mark (!) to the first, opening set of double dollar signs, like so: $$\omega$$ which renders as

$\omega$

Refer to the the plugin homepage for more details.

Enjoy!