IEEE Solid-States Circuits Magazine - Summer 2019 - 36

which leads to a unity harmonic feedback factor (b 2f0 = 1) . The harmonic
voltage presented at the gate induces
an extra harmonic current that is almost out of phase with the original one
generated through f0 - 2f0 nonlinear
conversion (which is supposed to be
fully extracted to output). That is another reason for the low output power
of push-push oscillators. Shown in Figure 4, the harmonic output power at
300 GHz is four times smaller than the

optimal, which is associated with nearzero feedback (i.e., full drain-to-gate
harmonic isolation).
To achieve the first optimum gain
condition, in [31] a triple-push structure in 65-nm CMOS is used to match
the optimum phase of near 120° at
160 GHz. The measured third-harmonic power at 480 GHz (160 μW)
is approximately 8,000 times higher
than its silicon predecessors were before 2010 [28], [29]. In another work

Oscillator
1
βnf 0

Pout/Pout,max

vG,nf 0
vD,nf 0
G
D

0.6
0.4
0.2
0

S

inf 0

0.8

inf′ 0

Im 0
(β
2

Induced Harmonic Current

1
f0 )

(a)

-1 -1
(b)

0
)
( β 2f 0
Re

FIGURE 4: (a) The harmonic feedback factor that affects the net harmonic output power from
a transistor. (b) The simulated harmonic output power at 260 GHz of a 65-nm NMOS transistor with a varying harmonic feedback factor. In a push-push oscillator, Re (bnf0) is 1, and
Im (bn f0) is 0.

2f0

90°

g 11 + Re (A opt $ y 12)
1
=
, (1)
Z 0 sin { TL
Im (A opt)

Traveling Wave
+ -

f0
0°

[33], the optimum phase of the gain
is achieved using a lower fundamental frequency (where +A opt is close
to 180°) and higher harmonic order
(fourth). The measured power at
290 GHz is 0.76 mW.
To simultaneously achieve the optimum gain and harmonic isolation
for even higher output power, a selffeeding oscillator topology utilizing
wave synthesis is proposed [34]. The
basic schematic of such an oscillator
is shown in Figure 5, where a transmission line (TL) supporting traveling
wave is used as the transistor's oscillation feedback path. In addition, the
boundaries on two sides of the TL are
engineered through YG and YD to create proper reflections (hence, standing
wave). It is shown that both optimum
conditions can be obtained by controlling the patterns and relationship of
the traveling and standing waves inside the TL [32]. For the optimum gain
A opt at fundamental frequency, such
a wave can be synthesized when the
design parameters in Figure 5 comply
with the relationship

Standing Wave
180°

Z0, φTL

270°
0°

Hi-Z at 2f0
90°

2f0

Af0,opt

YD

YG
Active
Boundaries
Passive Boundaries

FIGURE 5: The basic schematic of a self-feeding oscillator (right) and the architecture of an eight-element radiator array at 260 GHz [32].

36

SU M M E R 2 0 19

IEEE SOLID-STATE CIRCUITS MAGAZINE



IEEE Solid-States Circuits Magazine - Summer 2019

Table of Contents for the Digital Edition of IEEE Solid-States Circuits Magazine - Summer 2019

Contents
IEEE Solid-States Circuits Magazine - Summer 2019 - Cover1
IEEE Solid-States Circuits Magazine - Summer 2019 - Cover2
IEEE Solid-States Circuits Magazine - Summer 2019 - Contents
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