```Supporting Information
Marco Grisi, Gabriele Gualco and Giovanni Boero
1
Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, CH-1015, Switzerland
2Q 4 2Q 2
1
1
- 4 2 (1  Q 2 )( 2 )
2
RC
RC
RC Rm RC
Ct 
,
2 2 (1  Q 2 )
Cm 
2
.
 RmQ -  Ct Q RC Rm -  2Ct RC Rm
2
2
(A.1)
For simplicity, we neglected the parasitic capacitance of the
LNA, whose impedance has to be compared to Rm/2. In our
system Rm/2=160 Ω and the impedance of the LNA parasitic
capacitance is about 1.1 kΩ at 300 MHz. Solving the circuit in
Fig. Aa and using (A.1) we obtain the relation between V and
i:
FIG. A Schematics representing tuned and matched probe in (a)
TX mode and (b) RX mode.
irms
SI.A Intrinsic gain and pulse length
Vrms
Rm RC
.
(A.2)
During excitation, the effective field is B1  Bu i sin 0t  2 .
Given that ϑ= γB1τ the pulse duration τπ/2 required to reach the
In this appendix we derive the expressions of the intrinsic gain
maximum signal can be written as:
Gint and pulse length τπ/2 in tuned and matched pulsed NMR
 /2
probes. Fig. A shows equivalent circuits of probes in both TX
and RX conditions. In Fig Aa we impose a voltage V across
 Rm RC
2 BuVrms
.
(A.3)
Equation (A.3) shows that choosing a large value for Rm would
the nodes a and a̅ and we are interested in the current through
be unattractive, while a high Bu helps in reducing the pulse
the coil i. In Fig Ab the NMR signal is represented by an elec-
length. Similarly, solving the circuit in Fig. Ab gives:
tromotive force induced in the coil and we want to calculate
Rm
.
4 RC
(A.4)
the voltage V’= GintV across the nodes a and a̅. The tuning and
V' V
matching capacitances, respectively Ct and Cm, are used to
From equation (A.4) we obtain Gint  V '/ V  Rm 4RC . As
transform the impedance of the coil. Being reactive elements,
we can see, a larger Rm would be convenient in reception since
no noise is added by them and we can assume that during im-
a large intrinsic gain guarantees that the noise coming from
pedance transformation the SNR is preserved. If we impose
the coil becomes dominant with respect to the noise of the
that the impedance Z of the circuit on the right side of the
front-end electronics nelec . This observation is evident also
nodes a and a̅ is equal to Rm (i.e., impedance matching condi-
writing the total input noise of the system, which is
2
.
nin  2kBTRm  nelec
tion) we obtain:
1
Mp2) , RL is the output resistance, γ is a technological constant
SI.B Integrated electronics design
approximately equal to 2/3, gmm is the transconductance of the
current mirror devices (Mp3, Mp4, Mp5, Mp6) ,Kfn and Kfp are
the flicker noise constants of n and p devices respectively, C L
and Ci are the sum of the capacitances connected to the output
The transistor level schematics of the main elements of the re-
and input nodes, including the MOS parasitics. Equation (B.1)
ceiver are shown in Fig. Ba-c. The dimensions of all the ob-
points out that, maximizing the input transconductance and
jects shown are listed in Table A. The main transistor level
designing the current mirror devices in strong inversion (i.e.
design challenge is to trade-off between the wide bandwidth
with small aspect ratio, small gm), it is possible to make neg-
(1-300 MHz) and low input referred noise (about 1 nV/ Hz
ligible the noise due to transistors other than the input trans-
) requirements. In integrated circuit high frequency operation
conductor. Furthermore, noises of cascode devices and load
(i.e. in the GHz range) is achieved by using small area transis-
resistances are negligible thanks to particular structure for the
tor sizes. Small devices have smaller parasitic capacitance and
former, and to the voltage gain division for the latter. After
hence better speed performance. On the other hand they have
this consideration we found the following a good design strat-
larger flicker noise with corner frequency in the MHz range
egy: to trade-off between noise and speed a gm/I ratio of 10 is
limiting their functionality for low frequency operation.
been chosen as a starting point for the input devices.3 The min-
Shown in Fig. Ba is the transistor level schematic of the low
imum input transistor area is set by the noise performances at
noise amplifier. The device amplifies the small NMR signal in
low frequency (flicker noise). The minimum transconductance
order to make the noise contribution of the following down-
is set by the thermal noise floor (i.e. for frequencies typically
conversion device (mainly the frequency mixer) negligible.
above 20 MHz).To maximize the transconductances per unit
For the external coil case the minimum input noise is about
area, the devices are designed with short lengths and large
1.8 nV/ Hz , set by the 160 Ω equivalent input impedance in
widths. The supply current is then used to tune the transcon-
matched conditions. Since the noise of a frequency mixer is in
ductance in order to achieve the wanted noise. After designing
the order of few tens of nV/ Hz ,1 the 39 dB gain of the LNA
the input transconductance, the resistive load is decided in
is enough to not deteriorate the SNR in the following circuitry.
function of the desired gain. Since the structure is fully differ-
The chosen scheme, inspired by Ref. [2], is a current reuse dif-
ential, a feedback has to be added to ensure the stability of the
ferential transconductance, loaded with a pseudo cascode. The
output common mode voltage. This is done by mean of tran-
voltage gain, input referred noise and main frequency pole can
sistors (Mn5, Mn6 Mp7, Mp7) which set the output dc voltage at
be expressed, in first approximation, by the following equa-
a level which is about 1 V. In figure Bb a double balance Gil-
tions:
bert cell mixer is shown. This active mixer is chosen among
A υ =  gm p +gm n  ×R L
f p1 =
f p2 =
others for its simplicity and for noise performances, which are
1
2πR L ×CL
better if compared with the passive counterpart. Transistors
Mn1,2 together with Rs1,2 act as transconductance, converting
gds p +gds n +gm B
the voltage signal coming from the LNA into a current. Tran-
(B.1)
2πCi
sistor Mn3-6, driven by the local oscillator, multiply the current
K fp
4k B Tγ
K fn
v =
+
+
+
gm p +gm n  WL n f  WL p f
2
n

4k B Tγgm m
 gm
p
+gm n 
2
+
K f gm m2
 WL m f  gm p +gm n 
2
signal by a square wave. The resulting signal is composed by
+
sinusoids with frequency equal to the sum and difference of
4k B TR L
A 2v
the one driving the mixer. The sum component is filtered out
by the load filter, leaving a sinusoid oscillating at the differ-
where gmp,gmn, gdsp and gdsn are the gate-drain and drain-
ence in frequency between the signal and the local oscillator.
source transconductances of the input devices (Mn1, Mn2, Mp1,
2
Again, the minimum size of the input devices is chosen to keep
equal to f p =1 2πR F C F is added to filter out the sum compo-
the input referred noise in a reasonable range (10 nV) and the
nent. In Fig. Bc the audio frequency amplifier following the
transistor Mn3-6 are sized to behave as hard switches when
mixer is detailed. The design rules considered to size the tran-
driven by a 1.5 V peak-to-peak square wave at 1 GHz. With
sistors are the same ones discussed for the pre-amplifier. A
this assumption the voltage gain can be written as
resistive feedback is then added to control voltage gain.
Av = 4R L πRs . At the output a low pass filter with frequency
LNA
Object name
Width (μm)
Length (μm)
Mn1, Mn2
350
0.18
Mn3, Mn4
70
0.13
Mn4, Mn6
40
0.13
Mp1, Mp2
840
0.18
Mp3, Mp4
150
0.2
Mp5
450
0.25
Mp6
290
0.25
Mp8, Mp8
45
0.25
Mp1, Mp2
15
0.4
Mp3, Mp4, Mp5, Mn6
50
0.13
MIXER
RS1,RS2
300 Ω
RL
2 kΩ
RF
100 kΩ
CF
20 pF
AF amplifier
Mn1, Mn2
100
3
Mn3, Mn4
30
0.3
Mp1, Mp2
70
4
Mp3, Mp4
60
0.5
Mp5, Mp6
35
4
RI1,RI2
6 kΩ
RF1,RF2
18 kΩ
RL
10 kΩ
RI1,RI2
400 Ω
CC1, CC2
3 pF
TAB. A Design physical dimensions.
FIG B: Detailed schematics of (a) LNA, (b) Mixer, (c) AF amplifier.
3
The transistor level schematic of the transmit-receive switches
is shown in Fig. C. The schematic shows how the interface
between transmitter and receiver is realized for one of the two
differential inverters chains. In the case shown, the total number of inverters is even and a few straightforward adjustments
have to be done to construct the other differential pair (whose
number of inverters is odd). When the control signal s=2.5 V
(s̅=0) we are selecting the RX mode and the inverter chain is
FIG C: Detail of transmit-receive switches
in stand-by. In the opposite configuration the inverters are
transmitting power to the probe and the switches on the re-
1
Behzad Razavi, RF microelectronics. (Prentice Hall New Jersey, 1998).
J. Anders, P. SanGiorgio, and G. Boero, J Magn Reson 209 (1), 1 (2011).
3
Willy MC Sansen, Analog design essentials. (Springer, 2007).
ceiver side protect the LNA.
2
4
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