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G16.4427 Practical MRI 1
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G16.4427 Practical MRI 1 – 16th April 2015
Outline
• Paper Review
• RF power amplifiers
• Dual-tuned coils
G16.4427 Practical MRI 1 – 16th April 2015
Paper Review
G16.4427 Practical MRI 1 – 16th April 2015
D.K. Sodickson, 2-26-09
Sidebar: Component coil
combinations in arrays
?
D.K. Sodickson, 2-26-09
Sidebar: Component coil
combinations in arrays
Optimal combination:
=
*
+
*
+
*
+
*
Sum of squares combination:
=
(
*
+
*
+
*
+
*
)
1/2
D.K. Sodickson, 2-26-09
Component coil combinations and
signal-to-noise ratio
Matched filter effect:
Unfiltered
Filtered
Coil #1
Coil #2
Coil #3
Coil #4
Sum
D.K. Sodickson, 2-26-09
Component coil combinations and
signal-to-noise ratio
Generalized quadrature effect:
D.K. Sodickson, 2-26-09
SENSE as a generalized optimal coil
combination
S
inverse
 S Ψ S  S Ψ
H
1
1
H
1
H
1
S
Ψ
no acceleration

 H 1
S Ψ S
Matched filter
combination
Noise
decorrelation
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
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
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?
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
Actual RF Pulse Parameters
G16.4427 Practical MRI 1 – 16th April 2015
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 20-300 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
G16.4427 Practical MRI 1 – 16th April 2015
Pulse Pre-Shoot, Post Pulse Backswing
Post pulse
backswing
Pulse
pre-shot
G16.4427 Practical MRI 1 – 16th April 2015
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 20-300 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
G16.4427 Practical MRI 1 – 16th April 2015
Pulse Transition Duration
Fall
time
Rise
time
G16.4427 Practical MRI 1 – 16th April 2015
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%
G16.4427 Practical MRI 1 – 16th April 2015
Overshoot, Rising/Falling Edge
Rising
pulse
overshoot
Pulse
falling
edge
Pulse
rising
edge
Falling
pulse
overshoot
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
Pulse Overshoot Ringing/Decay Time
Pulse
overshoot
ringing/dec
ay time
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
Pulse Tilt (Positive/Negative)
Pulse
tilt
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
Pulse Overshoot Ringing/Decay Time
Un-Blanked
noise
voltage
Blanked
noise
voltage
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
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)
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
RFPA Specifications: Power Domain
• The input power to the RFPA is swept across a
range of power levels (usually 30-40 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: 0.5-2 kW extremities (legs and arms), 4-8 kW
head, up to 35 kW whole body
– Higher field strengths: 10-20 kW is common
– Multi-channel: 4 kW (3T) and 1 kW (7T) per channel
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
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
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
G16.4427 Practical MRI 1 – 16th April 2015
Troubleshooting
Amplifier Performance Anomaly
Symptom
Excessive gain non-linearity
Slice profile distortion
Excessive phase non-linearity
Slice profile distortion
Excessive rise/fall time
Slice profile distortion
Gain instability
Image ghosting/shading
Phase instability
Image ghosting
Excessive pulse overshoot
Slice profile distortion
Spurious oscillation
Image artifacts/streaking
Low power output
Inability to achieve desired flip angle
G16.4427 Practical MRI 1 – 16th April 2015
Any questions?
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
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
G16.4427 Practical MRI 1 – 16th April 2015
Any questions?
G16.4427 Practical MRI 1 – 16th April 2015
See you next week!
G16.4427 Practical MRI 1 – 16th April 2015