Selective RF 90 Degree Pulse Gaussian Power Calculator

Model Gaussian pulse power with practical RF inputs. Adjust duration, coil calibration, margin, and losses. Export clean results for review, records, and lab notes.

Calculator Inputs

Degrees. Use 90 for a 90 degree pulse.
Milliseconds.
Milliseconds.
MHz per tesla.
Microtesla from calibration.
Watts used for reference B1.
Decibels.
Percent added to amplifier demand.
Percent for continuous average power.
Used for train energy.
mT/m. Use zero to skip thickness.
Watts.

Formula Used

The calculator models the Gaussian RF envelope as B1(t) = B1peak × exp(-(t - T/2)² / (2σ²)). The flip angle is θ = γ × ∫B1(t)dt.

The truncated Gaussian area is σ × √(2π) × erf(T / (2√2σ)). Therefore, B1peak = θ / (γ × area).

Coil power scaling uses Ppeak = Pref × (B1peak / B1ref)². Chain loss and margin are then applied to estimate amplifier demand.

RMS B1 uses the mean squared Gaussian shape. Pulse average power equals peak amplifier power multiplied by that mean squared shape. Energy equals pulse average power multiplied by pulse duration.

How to Use This Calculator

  1. Enter the desired flip angle. Keep 90 for a 90 degree pulse.
  2. Enter pulse duration and Gaussian sigma from your pulse design.
  3. Enter the gyromagnetic ratio for the selected nucleus.
  4. Add measured coil calibration using reference B1 and reference power.
  5. Add cable loss, switch loss, and a practical safety margin.
  6. Use duty cycle and pulse count for average power and energy checks.
  7. Press Calculate. The result appears below the header and above the form.
  8. Download CSV or PDF files for records and review notes.

Example Data Table

Case Duration ms Sigma ms Reference B1 microtesla Reference Power W Loss dB Margin %
Short selective pulse 2.00 0.45 10 100 1.5 20
Balanced pulse 3.00 0.65 10 100 1.5 20
Longer selective pulse 5.00 1.10 10 100 1.5 20

Selective RF Gaussian Pulse Power Planning

A selective RF 90 degree pulse is used when a system needs rotation near a chosen resonance band. A Gaussian envelope is common because it starts smoothly, reaches a defined peak, and ends smoothly. This shape reduces abrupt transitions that may broaden excitation or stress hardware.

This calculator estimates the peak RF field required to create a target flip angle. It also converts that field into power using a practical coil calibration. The calibration says how much B1 is produced by a known power level. The tool then scales power with the square of the field ratio.

The duration and sigma values define the pulse shape. A longer pulse gives more time for rotation, so the peak field can fall. A wider sigma gives a fuller Gaussian area, but it can also change the bandwidth estimate. The truncation correction keeps the calculation tied to the entered duration, not to an infinite Gaussian.

The result includes peak B1, RMS B1, peak power, pulse average power, energy per pulse, train energy, estimated bandwidth, and optional slice thickness. RF chain loss and safety margin are included because real cables, switches, and matching networks waste power. The amplifier percentage helps compare the demand against a chosen limit.

Use the calculator as a planning aid, not as a safety certificate. Actual MRI, NMR, spectroscopy, or communications hardware may require vendor calibration, probe tuning, duty cycle limits, and SAR review. The estimate is most useful when the calibration was measured with the same coil, load, frequency, and pulse setup.

Good inputs improve the answer. Measure the reference B1 and reference power carefully. Use a realistic pulse length. Enter sigma based on the shape file or pulse design notes. Add losses in decibels when the reference point is not at the coil. Add margin when tuning may drift.

The CSV and PDF options make it easier to document setup choices. Keep records with sample, coil, frequency, and operator notes. This supports repeatable pulse planning and safer reviews.

Before use, compare the result with a low power test and a measured nutation curve. Small calibration errors can grow quickly because power follows a square law. Document temperature, loading, and frequency shifts when results are critical for later checks.

FAQs

What does this calculator estimate?

It estimates peak B1, RMS B1, peak amplifier power, average power, pulse energy, bandwidth, and optional slice thickness for a truncated Gaussian RF pulse.

Why is coil calibration required?

Power depends on the coil, sample loading, tuning, cabling, and frequency. Calibration connects a known B1 value to a known power level, allowing realistic scaling.

Can I use this for a pulse other than 90 degrees?

Yes. Change the flip angle field. The default is 90 degrees, but the same formula can estimate other flip angles.

What does Gaussian sigma mean?

Sigma controls the Gaussian width. A larger sigma gives a broader envelope within the pulse duration and changes area, RMS power, and bandwidth.

Why include RF chain loss?

Cables, switches, filters, and connectors can reduce delivered power. Adding loss helps estimate the amplifier output needed to achieve coil power.

Is the PDF export generated on the server?

Yes. The page creates a simple downloadable PDF summary from the calculated result without requiring an external PDF library.

Does this calculator check SAR limits?

No. It estimates power and energy only. SAR, tissue limits, regulatory rules, and system duty limits require separate safety review.

Why does average power differ from peak power?

A Gaussian pulse is not at peak amplitude for the whole duration. Average pulse power uses the mean squared shape across the pulse.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.