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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