IEEE Solid-States Circuits Magazine - Fall 2020 - 99

Vtune
L2
Varactor
l1
+
V1

Bipolar

k
L1

k
C1

L1

L2

VCC

C2
Vtune

-
L2
CMOS

Vbias

k
L1

VDD

FIGURE 18: The varactor coupling using a magnetic transformer.

phase noise that, for a target ampli-
tude of oscillation V1, is obtained at
the price of higher current consump-
tion. It should be noted that, as shown
by (29), the transformer's voltage gain
A v21 can be leveraged to decrease the
excess noise factor F in a two-port
oscillator (as long as the voltage swing
at the secondary does not exceed the
voltage ratings of the active devices).
A useful application of magnetic
transformers in the design of inte-
grated oscillators is to implement a
low-loss varactor coupling to the tank
[33], [34]. This is particularly useful at
millimeter-waves (mm-waves), where
the quality factor of capacitors signifi-
cantly decreases. Examples of varac-
tor coupling in the context of bipolar
or CMOS technologies are illustrated
in Figure 18. The use of transformer
coupling allows one to explore the
entire tuning curve of the varactor
with a single supply voltage. More-
over, the transformer's turn ratio can
be leveraged to decrease the swing on
the varactor. This is especially useful
for pn-varactors to avoid their turning
on during part of the oscillation cycle,
heavily degrading the quality factor of
the resonator. The use of the trans-
former coupling does not remarkably
change the way the oscillator is tuned.
In this application of the transformer,
the capacitance at the primary wind-
ing is typically just a small parasitic.
If C 1 % C 2, then p & 1 and ~ L . ~ 2.

Hence, the oscillator tuning is as in a
conventional LC tank.
The key feature of a doubly tuned
resonator is the presence of two
parallel resonances. The resulting
modes of oscillation at ~ L and ~ H
can be leveraged to expand the tun-
ing range of an oscillator [5], [8], [29],
[31]. Another possibility is to set ~ H
to the second harmonic of the oscil-
lation frequency to decrease the 1/f
noise upconversion into phase noise
[35], [36]. Yet another option is to
have simultaneous resonances at the
fundamental and third harmonic,
which increases the slope of the
voltage waveform, resulting in the
so-called class-F oscillator [37]. In
addition, tuning ~ H to the third har-
monic enables the extraction of the
third harmonic, realizing an implicit
frequency multiplication [7], [38].

Conclusions
The lack of high-permeability mate-
rials and the geometric constraints
in microelectronic planar processes
limit the obtainable magnetic cou-
pling k and turn ratio n of integrated
transformers. The magnetizing and
leakage inductances are never neg-
ligible, so it is of paramount impor-
tance to try and embed them into the
design of the circuit. Magnetically
coupling inductors also allows one to
decrease the coil footprints and helps
implement lumped-element ver-

sions of distributed passive circuits.
Transformers are key to amplifiers'
designs, especially at mm-waves,
because they provide low-loss ac cou-
pling, yield impedance transforma-
tion, and enable power combining.
Finally, magnetic transformers do not
increase the resonators' quality fac-
tor per se, but they are useful to make
oscillators with low phase noise and
wide tuning range.

Acknowledgments
I would like to thank Prof. Shuhei
Amakawa and Prof. Ali Sheikholesl-
ami for their valuable feedback and
fruitful suggestions. This article
is an abridged version of a tutorial
given at the IEEE International SolidState Circuits Conference in Febru-
ary 2020 [14].

References

[1]	 F. Wang, T. Li, and H. Wang, " A highly
linear super-resolution mixed-signal
Doherty power amplifier for high-effi-
ciency mm-wave 5G multi-Gb/s communi-
cations, " in Proc. IEEE Int. Solid-State Circuits Conf. (ISSCC), 2019, pp. 88-90. doi:
10.1109/ISSCC.2019.8662497.
[2]	 H. Liu et al., " A 265μW fractional-N digi-
tal PLL with seamless automatic switch-
ing subsampling/sampling feedback
path and duty-cycled frequency-locked
loop in 65nm CMOS, " in Proc. IEEE
Int. Solid-State Circuits Conf. (ISSCC),
2019, pp. 256-258. doi: 10.1109/ISSCC.
2019.8662374.
[3]	 S. Pellerano et al., " A scalable 71-to-76GHz
64-element phased-array transceiver
module with 2×2 direct-conversion IC
in 22nm FinFET CMOS technology, " in
Proc. IEEE Int. Solid-State Circuits Conf.
(ISSCC), 2019, pp. 174-176. doi: 10.1109/
ISSCC.2019.8662496.
[4]	 Z. Yue et al., " A 52% peak-efficiency >1W
isolated power transfer system using ful-
ly integrated magnetic-core transformer, "
in Proc. IEEE Int. Solid-State Circuits Conf.
(ISSCC), 2019, pp. 244-246. doi: 10.1109/
ISSCC.2019.8662301.
[5]	 A. Bhat and N. Krishnapura, " A 25-to38GHz, 195dB FoMT LC QVCO in 65nm LP
CMOS using a 4-port dual-mode resonator
for 5G radios, " in Proc. IEEE Int. Solid-State
Circuits Conf. (ISSCC), 2019, pp. 412-414.
doi: 10.1109/ISSCC.2019.8662502.
[6]	 C. Lim, J. Yin, P. Mak, H. Ramiah, and R.
P. Martins, " An inverse-class-F CMOS VCO
with intrinsic-high-Q 1st- and 2nd-har-
monic resonances for 1/f 2-to-1/f 3 phasenoise suppression achieving 196.2dBc/
Hz FOM, " in Proc. IEEE Int. Solid - State Circuits Conf. (ISSCC), 2018, pp. 374-376. doi:
10.1109/ISSCC.2018.8310340.
[7]	 Y. Hu, T. Siriburanon, and R. B. Staszews-
ki, " A low-flicker-noise 30-GHz class-f23
oscillator in 28-nm CMOS using implicit
resonance and explicit common-mode
return path, " IEEE J. Solid-State Circuits,
vol. 53, no. 7, pp. 1977-1987, 2018. doi:
10.1109/JSSC.2018.2818681.

	 IEEE SOLID-STATE CIRCUITS MAGAZINE	

FA L L 2 0 2 0	

99
IEEE Solid-States Circuits Magazine - Fall 2020

Table of Contents for the Digital Edition of IEEE Solid-States Circuits Magazine - Fall 2020
