1. G Practical MRI 1
Transmit Arrays

2. Outline
Paper Review
RF power amplifiers
Dual-tuned coils

3. Paper Review

4. Sidebar: Component coil combinations in arrays?

5. Sidebar: Component coil combinations in arrays
= * * * *
Optimal combination:
Sum of squares combination:
=( * * * * )1/2

6. Component coil combinations and signal-to-noise ratio
Matched filter effect:
Sum
Coil #2
Coil #3
Coil #4
Unfiltered
Coil #1
Filtered

7. Component coil combinations and signal-to-noise ratio
Generalized quadrature effect:

8. SENSE as a generalized optimal coil combination
Matched filter
combination
Noise
decorrelation

9. RF Power Amplifiers
RF Power Amplifiers (RFPAs) are a vital sub-system of any NMR spectrometer or MRI scanner
The sole purpose is the amplification of the RF pulse
Many power amplifiers may be required to achieve higher power output levels
Divider/combiner networks sum multiple stages
If the RFPA was ideal, the output would be an exact replica of the input waveform with greater amplitude
Conventional RFPA are not ideal and distort the signal

10. RFPA Architecture
Pre-Driver and Driver are low power amplifier stages that raise the power level of the input signal from mW to a level high enough to drive the high power PA sections
Directional coupler separates out proportional samples of forward and reflected power for internal/external power monitoring and fault detection
The microcontroller is a micro-computer that continuously runs a fixed program loop that monitors several vital operating parameters (e.g. DC voltages, currents, pulse width, etc.) If there is a risk of damage, it will put the system into fault mode
The DC power supply converts AC line voltages into DC voltages that are suitable to operate the Pre-Driver, Driver, Power Amplifiers and microcontroller

11. Actual RF Pulse
It takes 19 parameters to characterize a pulse that has been through a non ideal amplifier
It takes 4 parameters to define an ideal RF pulse. What are they?

12. Actual RF Pulse
It takes 19 parameters to characterize a pulse that has been through a non ideal amplifier
It takes 4 parameters to define an ideal RF pulse:
Amplitude
Frequency
Pulse width
Duty factor

13. Actual RF Pulse Parameters

14. RFPA Specifications: Time Domain
We want very high RF power pulses with precise fidelity only for short periods of time
Maximum pulse width (during which the RFPA can put out maximum power) is ms for MRI
Average power requirements (duty factor) ~10-15% maximum
Pulse pre-shoot, post pulse backswing
Distortion occurs after an RFPA has been un-blanked (or RF pulse is terminated)
Appears as half or more cycles of a low frequency signal superimposed on the un-blanked noise voltage
Low frequency, so it will be filtered out by the transmit coil

15. Pulse Pre-Shoot, Post Pulse Backswing
pre-shot

16. RFPA Specifications: Time Domain
Very high RF power pulses with precise fidelity for short periods of time
Maximum pulse width (during which the RFPA can put out maximum power) is ms for MRI
Average power requirements (duty factor) ~10-15% maximum
Pulse pre-shoot, post pulse backswing
Distorsion occurs after an RFPA has been un-blanked (or RF pulse is terminated)
Appears as half or more cycles of a low frequency signal superimposed on the un-blanked noise voltage
As low frequency, it will be filtered out by the Tx coil
Rise, fall time (transition duration)
Time to transition from 10% to 90% of the voltage waveform
Specification for MRI: 250 nsec to 10 μsec

17. Pulse Transition Duration
Fall
time
Rise
time

18. RFPA Specifications: Time Domain
Overshoot, rising/falling edge
Distortion occurs from inductively stored energy within the RFPAs circuitry (transition from zero to full power in ~100 ns  voltage spike due to large current changes in inductors get superimposed on the RF pulse)
Specification for MRI: < 13%

19. Overshoot, Rising/Falling Edge
pulse overshoot
Pulse
falling edge
Pulse rising edge
Falling pulse overshoot

20. RFPA Specifications: Time Domain
Overshoot, rising/falling edge
Distortion occurs from inductively stored energy within the RFPAs circuitry (transition from zero to full power in ~100 ns  voltage spike due to large current changes in inductors get superimposed on the RF pulse)
Specification for MRI: < 13%
Pulse overshoot ringing/decay time
Energy being fly between inductive and capacitive circuits in the RFPA generates a lower frequency dumped sinusoidal wave that is imposed on the RF pulse after the rise time and modulates its amplitude
Specification: time for the amplitude modulation to drop to less than 5% of peak RF pulse amplitude < 5 μsec

21. Pulse Overshoot Ringing/Decay Time

22. RFPA Specifications: Time Domain
Overshoot, rising/falling edge
Distortion occurs from inductively stored energy within the RFPAs circuitry (transition from zero to full power in ~100 ns  voltage spike due to large current changes in inductors get superimposed on the RF pulse)
Specification for MRI: < 13%
Pulse overshoot ringing/decay time
Energy being fly between inductive and capacitive circuits in the RFPA generates a lower frequency dumped sinusoidal wave that is imposed on the RF pulse after the rise time and modulates its amplitude
Specification: time for the amplitude modulation to drop to less than 5% of peak RF pulse amplitude < 5 μsec
Pulse tilt (positive or negative)
Gain change due to temperature increase in “on” RF transistors
Specification for MRI: < 8% over 20 ms rectangular pulse

23. Pulse Tilt (Positive/Negative)

24. RFPA Specifications: Time Domain
Long term amplitude/phase stability
Ideally would amplify every pulse exactly the same way
Changes in environment (e.g. temperature) can alter RFPAs
Specifications for MRI: amplitude < 0.2 dB, phase < 3 degrees over 24 hours at constant temperature
Phase error over-pulse
Occurs as a phase shift across the duration of a rectangular pulse in cases when the pulse tilt is substantial
Specification: < 5 degrees across a 10 msec pulse width
Un-Blanking, Blanking propagation delay
To reduce electronic noise during signal acquisition, the output stage of an RFPA are shut off
Delay measures the ability of an RFPA to rapidly turn on/off
Specification for MRI: 2 μsec

25. Pulse Overshoot Ringing/Decay Time
Un-Blanked noise voltage
Blanked noise voltage

26. RFPA Specifications: Frequency Domain
Generic frequency domain specifications
The bandwidth is the range of frequencies for which the RFPA complies with output power, linearity, etc.
Power gain
Specification: maximum peak power when maximum output power is required
Gain flatness
The wider the bandwidth the harder is to maintain constant power gain  flatness at key frequencies
Specifications: broadband = ± 3 dB, nuclei centered = ± 0.2 dB at ± 500 kHz

27. RFPA Specifications: Frequency Domain
Harmonic content
Practical RFPAs are not perfectly linear  output frequency spectrums also at integer multiples of the input frequency
Mostly filtered out by the transmit coil
Specification: even/odd order harmonics = -20 db/-12 dB
Spurious RF output emissions (oscillation)
Erratic frequency components that the RFPA puts out (e.g. DC feed that couples RF power from output to input)
Specification: < -50 dBc
Input VSWR
How close the input impedance is to an ideal 50 Ω resistor
Specification: < 2:1 (perfect match = 1:1)

28. RFPA Specifications: Frequency Domain
Output noise (blanked)
To minimize electronic noise, the bias of the transistors of the final stages of power amplification are shut off (there will still be some tolerable noise output)
Specification: -20 dB over thermal noise
Noise Figure
In applications where RFPA is transmitting at one frequency and RF receivers are listening at another, the less NF an RFPA has, the less will interfere with this second frequency
Specification: < -10 dB

29. RFPA Specifications: Power Domain
The input power to the RFPA is swept across a range of power levels (usually db)
E.g.: if an RFPA is driven to full power at 0 dBm input (i.e. 1 mW), the unit will be tested for input -40 to 0 dBm to check for phase linearity and gain
RF power output
1T-3T: kW extremities (legs and arms), 4-8 kW head, up to 35 kW whole body
Higher field strengths: kW is common
Multi-channel: 4 kW (3T) and 1 kW (7T) per channel

30. RFPA Specifications: Power Domain
Gain linearity
Defined in terms of dynamic range (from maximum specified output power level to some dB down from such level)
Specification: ± 1 dB gain variation over 40 dB dynamic range
Phase linearity
Although it takes few nanoseconds for the signal to go from input to output of the RFPA, there is a propagation delay
In ideal case the phase shift is constant across the dynamic range
Phase non-linearity is a due to parasitic junction capacitance present in all types of RF power transistors (change with output power)
Specification: ± 7.5 degrees phase variation over 40 dB dynamic range

31. Gain Linearity
Pulse sequences can contain RF waveforms that have precisely proportioned amplitude ratios, which can change dramatically in case of severe deviation from ideal gain linearity
In the non-ideal case, the transfer function changes over the dynamic range of the amplifier  power levels will be amplified by different power gain factors

32. Troubleshooting Amplifier Performance Anomaly Symptom
Excessive gain non-linearity
Slice profile distortion
Excessive phase non-linearity
Excessive rise/fall time
Gain instability
Image ghosting/shading
Phase instability
Image ghosting
Excessive pulse overshoot
Spurious oscillation
Image artifacts/streaking
Low power output
Inability to achieve desired flip angle

33. Any questions?

34. Dual-Tuned Coils
A major problem of implementing multinuclear MRI is the construction of a probe capable of operating at more than one frequency
To make a single-tuned coil resonant, we normally add a tuning circuit (a capacitor in series with the coil):
In order to multiple tune a coil, we need to make the reactance curve of the tuning network cross the anti-reactance curve of the coil more than once

35. Double Resonant Circuit
A useful tuning network consists of a parallel LC trap in series with the tuning capacitor network
The reactance, as a function of frequency, will begin capacitive, then pass through a pole (trap resonant frequency) and then become capacitive again
The reactance curve crosses the anti-reactance curve of the coil twice  two resonances are established

36. Matching
Normally a reactive element is added in parallel to the series tuned network so that the input impedance to the entire network is real and equal to the generator impedance
For dual-tuned coil, we can use a parallel LC matching network
At the low frequency C is large enough so that we may consider only the inductor and adjust its value for proper matching
The capacitor can then be tuned so that the parallel combination of C and L has the required reactance for matching at the higher frequency

37. Example: Dual-Tuned Birdcage at 1.5 T
The fourth harmonic of the sodium frequency is very close to the proton frequency at 1.5 T (67.8 MHz vs. 64 MHz)
It is challenging to decouple the two channels in a birdcage
Modified inductive coupling circuits (with baluns) are used to provide better decoupling
The trap circuit method is used to obtain identical current distributions for both resonance frequencies
Same B1 field distribution

38. Any questions?

39. See you next week!