IEEE Solid-States Circuits Magazine - Summer 2019 - 37

where Z 0 and { TL are the impedance and electrical length of the TL,
respectively, and g 11 and y 12 are
the Y-parameters of the transistor.
At the second-harmonic frequency,
the length of the TL (2{ TL) is chosen
to be nearly quarter-wave. [Note that
in (1), Z 0 couples with { TL, which
enables the relatively free selection of
{ TL .] Such a quarter-wave transformer transforms the low impedance at
the gate (due to large Cgs) into a much
higher one presented on the drain
side. Therefore, the high impedance
keeps the generated harmonic signal
from flowing back to the gate, thus creating effective isolation. In a 260-GHz,
65-nm CMOS oscillator array as shown
in Figure 5 [34], eight differential selffeeding oscillators are coupled with
phase synchronization, enabling the
power combining of their secondharmonic radiation in free space. The
radiation is through an on-chip, broadband slot-antenna array implemented
using the CMOS metal layers. An external high-resistive, hemispheric silicon
lens is attached to the back of the chip
to further enhance the backside radiation coupling into the air. This radiator
array has a measured radiated power
of 1.1 mW, which is the highest among
all THz/sub-THz CMOS radiators to
date. The chip can also modulate the
radiation with ultranarrow (~45 pS)
pulses to generate broadband spectrum (~25 GHz), which is useful for
THz spectroscopy.

Frequency Multiplier
Although a harmonic oscillator is a selfsustaining circuit that does not require
external input, it suffers from narrow
output bandwidth due to the increasingly significant transistor parasitic
capacitance, which is normally part of
the resonance tank. The variable part of
the tank, consisting of an MOS varactor,
is therefore smaller. To overcome this
disadvantage, we can implement oscillators at a lower frequency (i.e., wider
tuning range) and then feed the signal
into a frequency multiplier to generate
a broadband THz frequency.
To increase power efficiency, it
is critical to prevent leakage of the

fundamental signal at the output, as
well as the harmonic signal at the input. As a very straightforward solution, dedicated frequency filters are
often employed at the input and output. In THz design, these filters are
frequently implemented using quarter- or half-wavelength transmission
stubs [35], [36]. However, there are
two problems related to such isolation
methods. First, these filters are quite
bulky in terms of wavelength and are
lossy, especially the output high-pass
filters at harmonic. [The output filter is
designed to block the fundamental signal at f0 . Therefore, it often consists of
multisectional quarter-wave resonators at f0, which means the harmonic
signal (e.g., second harmonic) experiences several long, half-wavelength
lines before reaching the output.] Second, because they are resonance-type,
these filters also limit the bandwidth
of the multipliers, so alternative signal-filtering methods are preferred.
While Schottky diodes are widely
used in waveguide-housed multipliers
[1], [37], MOS or heterojunction bipolar transistors are adopted in almost
all previous silicon-based THz frequency multipliers due to their process compatibility [38], [39]. However,
this causes additional large dc power
consumption. To solve this problem,
next we introduce a design based on
MOS varactors, a passive variable
capacitor available in all CMOS technologies [9]. In a standard 65-nm bulk
CMOS process, the dynamic cutoff
frequency of the device is as high as
870 GHz, which enables us to efficiently
generate a THz signal without dissipating any dc power. However, compared
to transistors, the one-port MOS varactor does not provide any isolation
between the input and output signals, increasing the challenge for the
signal-filtering design mentioned previously in this section.
Instead of filtering the input/output signals based on their frequencies, in our design we separate them
based on their wave modes. Such a
concept is applied to the design of
a 480-GHz CMOS doubler. Shown in
Figure 6, this doubler is based on

a partially coupled ring structure.
Through magnetic coupling, the input signal at f0 is injected into the
ring with a differential pattern (unbalanced-wave mode). The two branches
of the signal travel along the left half
of the ring and are absorbed by the
varactor pair. On the output node of
the ring, because the two signals are
out of phase, a virtual ground is created that reflects back the signals.
The signal at f0 is therefore blocked
from the output.
When the fundamental signals are
doubled (in terms of frequency and
phase) by the nonlinear capacitors,
the two second-harmonic signals in
the two branches become in phase
(balanced-wave mode). They travel
along the right half of the ring until they are extracted and combined
at the output. In the left side of the
ring, the magnetic fields created by
the harmonic signals cancel each
other. Therefore, the isolation of the
second-harmonic signal at the input
is also obtained. Thanks to wavemode filtering, this doubler structure is very compact and efficient.
The chip, fabricated using 65-nm
CMOS, occupies only 120 # 250 nm 2,
excluding pads. In the measurement
(Figure 7), the chip is able to provide
230-μW power at 480 GHz with a conversion efficiency of 3.7%. Currently,
the output power is limited only by
the maximum available power of the
input testing source. Given a larger
input, we expect to obtain a nearly
1-mW output before the breakdown
of the MOS varactors. To the best our
knowledge, this doubler has the highest operational frequency among all
CMOS doublers.
As mentioned previously, one advantage of frequency multipliers over
harmonic oscillators is their broadband
nature. Such an advantage, however, is
offset if conventional topologies with
dedicated filters and resonant-type
matching networks are used. Fortunately, as shown in Figure 6, most of
the input and output signals are in the
form of traveling wave along the TLs.
The simulated -3-dB bandwidth of the
480-GHz doubler is as high as 70 GHz

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IEEE Solid-States Circuits Magazine - Summer 2019

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