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Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits with Metamaterials by Yang Shang, Hao Yu

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Chapter 11
In-Phase Detect i on
11.1 Introduction
In this section, an in-phase coupled CON architecture is proposed to improve
the sensitivity of SRX. As shown in Figure 11.1, the input power is amplified
by two oscillators, which are coupled in phase in a positive feed-back loop.
Then, the output voltage envelope is detected, indicating the input power
level. The main design challenge is how to realize in-phase coupling between
two oscillators.
The key idea of this paper is using a zero phase shifter (ZPS) to couple two
quench-controlled oscillators in phase. Compared to the transformer-coupling
metho d [95], the ZPS approach does not introduce the extra phase between
two oscillators, as shown in Figure 11.1(a). As a result, the SRX sensitivity
can be improved in terms of bo th reduced noise figure (NF) and increased
oscillator y amplification.
The proposed SRX with ZPS-coupled CON is designed in 65nm CMOS at
131.5GHz with a core area of 0.06mm
2
. The c ircuit measurement shows that
the receiver features a sensitivity of -84dBm, a noise equivalent power (NEP)
of 0.615fW/Hz
0.5
, a NF of 7.26dB and a power of 8.1 mW.
11.2 SRX Sens itivity Enhancement by ZPS-
Coupled CON
In this section, the fundamentals of the SRX circuit are described at first and
then, the sensitivity enhancement by the ZPS-coupled CON is discussed.
251
252 Design of CMOS Millimeter-Wave and Terahertz Integrated Circuits
ZPS
LNA
LC-tank-I
oscillator
LC-tank-II
oscillator
Envelope
detector
Quench signal
t
V
q
Quench signal
V
dc
0
E F
t
E
F
t
Input power
V
d
V
p
(a)
t
V
d
t
Input power P
1
Input power P
2
t
0
0
0
V
p1
V
p2
V
p1
V
p2
P
1
P
2
P
1
>P
2
(b)
Figure 11.1: (a) Proposed SRX structure, in-phase output (E,F), and
sin-wave quench signal; (b) envelop e shape response (V
P
) of oscillator
under different input power, and envelope detector output (V
d
).
In order to understand the sensitivity enhancement from the coupling of
two quench-controlled oscillators, one can apply the feedback model in a linear
time variant (LTV) analysis of SRX [9 4]. A simplified circuit model as well as
its feedba ck model are shown in Figure 11.2 (a) for conventional SRXs with
a single quench-controlled oscillator. Its time-varying transfer function is
Z
T V
(s, t) =
Z
0
ω
0
s
s
2
+ 2ζ(t)ω
0
s + ω
2
0
(11.1)
where ω
0
is 1/
LC, Z
0
is
p
L/C, and is damping function:
ζ (t) = ζ
0
(1 G
m
(t) R) = ζ
dc
+ ζ
ac
(11.2)
where ζ
0
is a constant.
Note that the receiver’s behavior is mainly determined by AC character-
istics of the damping function [94].
When the damping signal ζ (t) in each quench cycle is a ramping signal
ζ
ac
(t) = βt, the gain function and the sensitivity function g (t) of the SRX
become
µ (t) = κe
1
2
ω
0
βt
2
(11.3)
In-Phase Detection 253
L C
Z
RLC
(s)
Vo(s,t)
G
m
(s)
i
a
(t)
i
a
(s)
G
m
(t)Vo(t)
R
o
ω
ω
o
ω
o
ω
o
(a)
i
a
(t)
G
m2
(t)V
2
(t)
L
z
C
z
L
z
V
1
(s,t)
i
a
(s)
V
2
(s,t)
G
m2
(s)
Z
C
(s)
Z
C
(s)
G
m1
(s)
G
m1
(t)V
1
(t)
R
R
Tank-I
Tank-II
ZPS
Z
RLC
(s)
(b)
Figure 11.2: Traditional SRX circuit model and its feedback model;
(b) proposed S RX circuit model and its feedback model.
g (t) = κe
1
2
ω
0
βt
2
(11.4)
where β is the slope (G
m
R), a nd κ is a constant.
The simplified circuit and feedback loop model of the SRX with two cou-
pled q ue nch-controlled oscillators is shown in Figure 11.2 (b). Its transfer
function can be simplified as follows:
Z
NT V
(s, t) =
Z
RLC
(s)Z
RLC
(s)Z
C
(s)
[1 G
m1
(t) Z
RLC
(s)] [1 G
m2
(t) Z
RLC
(s)] Z
2
c
(s)
(11.5)
where Z
RLC
(s) is the impedanc e of the parallel resonator (or RLC), and Z
C
(s)
is the impedance of serial resona tor (or ZPS).
Note that G
m1
(t) and G
m2
(t) are de termined by the phase difference of
the injected signal between the two oscillators [89]. At the interested frequency
around ω
0
, the impeda nc e of seria l resonator (or ZPS) is much smaller than the
parallel resonator (or RLC). As such, equa tion (11.5) ca n be further simplified
as
Z
NT V
(s, t) =
Z
RLC
(s)
1 [G
m1
(t) + G
m2
(t) ]Z
RLC
(s)
(11.6)
where high-order terms a re neglected due to small value at the beginning of
the start-up.

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