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Super-regenerative Receiver
U.L. Rohde and A.K. Poddar
Synergy Microwave Corp., Paterson, NJ
This article describes the super-regenerative receiver (SRR), a device widely used
in short distance telemetry and remote control applications. The difficulty in modeling
the regenerative behavior served as the basis for “cut and try” methodology based on
results obtained from the simplified model using a conventional approach. This work
presents the SRR behavior to practical implementations by dynamically controlling the
injection-mode levels of the super-regenerative oscillator (SRO) for optimum sensitivity
and dynamic ranges.
Integrated Circuit (IC) designers have the luxury of taking for granted that the
incremental cost of a transistor is essentially zero, which has given liberty to the large
device count circuits that are prevailing today. This is a recent development, but it really
was not all that long ago when the economics of circuit design were fundamentally based
on the number of device counts, and often the designer was restricted by the relatively
expensive active device to try to get blood (or at least rectification) from a stone.1-13
It is
amazing that in the early 1920s, Edwin Armstrong devised a super-regenerative receiver
circuit using few components that trade log of gain for bandwidth, contrary to the
conventional wisdom that gain and bandwidth should trade off more or less directly. The
reduction of the number of the device components is not only cost-effective, but also
improves reliability.
The characteristics of the super-regenerative receiver to generate large-signal gain
at very low bias currents and the ability to operate above the cut-off frequency (fT) of the
RF device make it attractive and the preferred architecture for integrated ultra-low power
wireless receivers. Figure 1 depicts a 1940’s 500 MHz SRR, which is bulky and require
manual calibration, but the circuit operates above the device fT, which was an astonishing
accomplishments in those days.12-13
Fig.1. A 1940’s 500 MHz Super-regenerative Receiver (vintage two-tube super-
regenerative detector)12
The phenomenon of super-regenerative detection has been the main focus
of the research, and it is still an open issue despite significant gains in practical
experience and modern CAD tools for design. The SRR circuit uses just a few
components, and its basic design is simple, but detailed analysis is complex, due to the
time varying and nonlinear characteristics of the receiver circuit.
Super-regenerative receivers have been used for many decades, and are still
manufactured in large quantities for short-distance data exchanges. Although an SRR has
advantages of high gain, simplicity, low cost, low power consumption and constant
demodulated output over a wide range of input signal levels, it has also drawbacks of
inherent frequency instability.
Figure 2 shows the typical block diagram of a super-regenerative receiver, which
consists of a matching network, an isolation amplifier, an amplifier with time varying
loop gain and a bandpass feedback network forming a regenerative oscillator.13
Antenna
Passive
Matching
NetworkBuffer
Amplifier
A(t)
Time varying
loop gain
Band Pass Positive
Feedback Network
SRO
Figure 2. A typical bloc diagram of super-regenerative receiver (SRR)
The buffer amplifier between the antenna and the SRO (super-regenerative
oscillator) performs the following functions: It reduces the RF leakage of the oscillation
signal to the antenna, it provides an input match to the antenna via the passive matching
network, and it injects the RF input signal current into the oscillator tank without adding
significant loading to the SRO. The time varying nature of the loop gain is designed such
that the SRO transconductance periodically exceeds the critical values of the transistor
transconductance gm necessary to induce instability. Consequently, the SRO periodically
starts up and shuts off. The periodic shutdown of the SRO is called “quenching”.
The start-up time of a SRO (the time from enabling the oscillator until it reaches
its saturation voltage VSRO,) can be described by:
=
2
log
n
SROriserise
v
Vt τ (1)
where τrise is the time constant of the exponentially increasing oscillation envelope,
VSRO is the zero-peak RF voltage of the saturated oscillator, and vn is thermal noise
generated due to resonator tank and active devices. From Equation 1, the start-up time of
the SRO is dependent on the instantaneous noise in the resonator, when the SRO loop
gain is unity (at the onset of oscillation).
Figure 3 exhibits the startup of the SRO in presence of thermal noise. Observing
that the startup time is very sensitive to low-level signals in the SRO tank, it becomes
obvious that this mechanism can be used to amplify any RF input signal.
Figure 3. A typical startup transient of SRO circuit in presence of thermal noise.
Although the conceptual block diagram of the SRR is of a compact size, power-
efficient and uses small device counts, the design methodology is not well defined, which
leads to a “cut and try” approach, based on results obtained from the simplified model
(see Equation 1). Moreover, the compact size of the SRR implies a small antenna, with
poor efficiency that degrades the sensitivity of the receiver. To achieve reasonably good
performance, a high sensitivity is required that conflicts with the circuit design
requirements for low power consumption.3
Figures 4 and 5 show the schematic of the super-regenerative front-end and a
photograph of the SRR die, which overcome the above problems and offers improved
sensitivity, but at the cost of an expensive 1.9 GHz BAW resonator.13
The BAW
resonator exhibits a thermal drift; therefore, additional compensation circuitry is required
for integrated solutions.
Figure 4. A typical schematic of the super-regenerative front-end [13]
.
Figure 5. Photograph of the SRR die13
This article describes a cost-effective methodology to improve the sensitivity of
the SRR with practical implementations by using mode-injection locking for optimum
sensitivity and dynamic range.
Theory
Figure 6 shows a typical SRR circuit that consists of the following basic
modules: Antenna, LNA (low noise amplifier), SRO (super-regenerative oscillator), ED
(envelope detector), AGC (automatic gain control), QO (Quench oscillator) and BBF
(baseband filter). The working principle is based on a repeated build-up and decay of the
self-oscillations in an SRO whose frequency is near or equal to the RF signal frequency
intercepted by antenna.
Cc
C1
C2
R CL
Noise-Free
2-Port
Bipolar
ibn
vbn
rb
'
icn
B C
E
inr
Vbe
CLNA
Antenna
SRO
VEnv
V
ED
QO
BPFVF
Resonator
B'
Active device with noise sources & feedback Capacitors
AGC
VRF
iRFVEnv
V0
iq
iAGC
v(t)
RF SignalVRF(t)
v(t): Input to SRO
∆v0(t): Output of SRO
Figure 6. A typical super-regenerative receiver (SRR) circuit.
As illustrated, the RF signal VRF is intercepted by the antenna and injected
through an LNA into the SRO module. The main objective of the LNA module is to
facilitate the impedance matching and the injection of the RF signal intercepted by
antenna into the SRO module. The LNA module optimizes the noise figure and prevents
the impedance variations in the antenna, caused by changes in the nearby environments,
from pulling the SRO frequency, thereby resulting in a loss of sensitivity. In addition, the
LNA module provides isolation to minimize the power injected back into the antenna due
to the building-up of self-oscillations by SRO module.
The AGC port is driven by QO, which stabilizes the gain of the LNA module so
that the SRO operating point can be dynamically controlled for build-up and dampening
of the self-oscillations. The start-up time of the SRO’s self-oscillations is proportional to
the amplitude and frequency of the input RF signal received through the antenna. The
gain of the SRO is periodically varied by QO signal (fq) for sampling the RF signal at the
point of maximum sensitivity. The demodulation is performed by rectifying the self-
oscillation voltage ∆V0 and then filtering the envelope voltage VEnv by the BPF.
The AGC loop is used to stabilize the amplitude of the VEnv by adjusting the bias current,
thereby enhancing the receiver’s input dynamic range.
Design Basis
Figure 7 shows a typical block diagram of the SRR circuit for formulating the
basic relationship and describing its regenerative behavior and sensitivity.8 As depicted,
the SRO module can be modeled as a selective network (SN), integrated with the quench
oscillator (QO) and a feedback through an amplifier for stable and sustained regenerative
actions.
SRO
∆v0LNA SN
Quench
Oscillator
vs(t)v(t) vFLPF
vEnv
Ka(t)
+
va(t)
ED
Feedback Amplifier
)(tς
vRF(t)
QO fq(t)
Antenna
vRF(t)
Figure 7. Simplified block diagram of the SRR.
The feedback amplifier module shows a variable gain Ka(t), which is controlled
by the quench signal ( fq) that forces the system to be alternatively stable and unstable.
The typical input signal v(t) of the SRO can be given in a single quench interval as
)(]cos[)()( 0 tnttpVtv cm ++= φω (2)
where Vm is the peak amplitude, pc(t) is normalized envelope of the SRO output, n(t) is
the additive Gaussian noise generated by the active devices of the receiver circuit
(described by the autocorrelation function )(]2/[)( tRn δητ = with the power spectral density
2/)( η=fGn).
The SRO output ∆v0(t) can be described by4-9
ττωττς dtsvtpKKtv
t
t
cs
a
)(sin)()()(2)( 0000 −=∆ ∫ &
(3)
where 0ς is the quiescent damping factor, s(t) is the sensitivity curve, K0 is the
maximum amplification and Ks is the super-regenerative gain.
The noise output ∆n0(t) can be given by
ττωττς dtsntpKKtn
t
t
cso
a
)(cos)()()(2)( 000 −=∆ ∫
(4)
From Equations 2 to 5, the signal to noise ratio (S/N) at the SRO output can be given
as8-9
∫∫
∫
=
=b
a
b
a
b
a
t
t
t
t
c
t
t
c
c
output
o
dsp
dspE
N
SSNR
τττ
τττ
η)()(
)()(
][22
2
(5)
where Ec is the average chip energy, which can be described by
∫=b
a
t
t
cc dpV
E ττ )(2
22
(6)
From Equation 5, the SNR of the SRO can be optimized using Schwarz’s inequality as
1
)()(
)()(
22
2
≤
∫∫
∫b
a
b
a
b
a
t
t
t
t
c
t
t
c
dsp
dsp
τττ
τττ
(7)
From Equations 5 and 7, [SNR]o, opt can be given by
)()(,][ tstpforE
SNR cc
opto ==η
(8)
The transfer function of the selective network (SN) can be described by
++=
2
000
2
000
2
2)(
ωωςως
ss
sKsG
(9)
From Equation 9, the characteristic differential equation of the SN can be given by
t
tvKtv
t
tv
t
tv s
∂∂
=+∂
∂+
∂∂ )(
2)()(
2)(
0000
2
00
002
0
2
ωςωως
(10)
where 0ς is the quiescent damping factor and K0 is the maximum amplification.
Figure 8 shows the typical parallel and series equivalent representation of the
SRO.
-Ga(t) +ν0(t)Li(t) C
Injected
Current
G0 v(t) C
L-Ra(t)R0
i0(t)
(a) Parallel RLC Circuit (b) Series RLC Circuit
Block Diagram v v0 K0 ζ0 ω0 Ka(t)
Parallel RLC i v0 1/G0 G0/(2Cω0) 1/√LC Ga(t)
Series RLC v i0 1/R0 R0/(2Lω0) 1/√LC Ra(t)
Figure 8. (a) Parallel and (b) Series equivalent representation of typical SRO module.
The feedback network can be described as )()()()( 0 tvtKtvtv as += , which can be represented by
the linear, time-variant, second-order differential equation
]
)()(
)()(
)([2)(
)(2
)(0
00000
2
00
002
0
2
t
tKtv
t
tvtK
t
tvKtv
t
tv
t
tv aa ∂
∂+
∂∂
+∂
∂=+
∂∂
+∂
∂ωςωως
(11)
t
tvKtv
t
tvt
t
tv
∂∂
=+∂
∂+
∂∂ )(
2)()(
)(2)(
0000
2
00
02
0
2
ωςωως for 0
)(→
∂∂
t
tKa
(12)
where )(tς is the instantaneous damping factor of the closed-loop system that can be
characterized as (see Figure 9)
)](1[)( 00 tKKt a−= ςς
(13)
ta tbo t
ζ(t)
ζ0
ζdc
ta tbo t
v0(t)
( )
sensitive
period
Build-up
starts here
Pulse generated in the
previous quench cycle
Pulse generated in the
current quench cycle
Figure 9. Typical plot of the damping function and envelope of the SRO output as
depicted in Figure 6.
The instantaneous quality factor Q(t) is6-8
)(2
1)(
ttQ
ς=
(14)
From Equations 9 to13, the general solution of the homogenous differential equation is
given by
)cos()()( 0 hchoh ttpVtv φω +=
(15)
where Vh and φh are the magnitude and the phase, respectively. The particular solution is
ττωττς dtsvtpKKtv
t
t
csop
a
)(sin)()()(2)( 000 −= ∫ &
(16)
τττως dspKb
a
t
t
cr )()(00 ∫=
(17)
∫
=−
bt
d
s eK 0
0 )( λλςω
(18)
∫
=−
t
bt
d
c etp
λλςω )(0
)(
(19)
∫
=
t
d
ets 0
0 )(
)(λλςω
(20)
where Kr is the regenerative gain, Ks is the super-regenerative gain, pc(t) is the
normalized envelope of the SRO output and s(t) is the plot of the sensitivity curve.
Figure 10 shows the plot of the s(t) and p(t) under sinusoidal quench, their
maximum values is unity at t = 0 for s(t) and t = tb for p(t).7-11
ta tbo t
ζ(t)
ta tbo t
Tq
A+
A-
tsa tsb Tq
s(t) p(t)1
Figure 10. Typical plot of the damping function, sensitivity curve and normalized
envelope
Super-regenerative Modes
There are two basic modes of operation: the logarithmic mode and linear mode
[12]. Figure 11 shows the typical modes of SRR operation: (a) detector output in the
linear mode, (b) detector output in the logarithmic mode and (c) RF input signal.
Figure 11. Modes of SRR operation: (a) Linear, (b) Logarithmic, and (c) RF Input
The linear mode is described by a linear relationship between the amplitude of the
RF input signal and the amplitude of the demodulated output. In this mode, SRO does not
reach its steady state during the quench period, due to a high quench frequency and/or a
low start-up current. However, the typical operation is made of a combination of both
modes; hence, it is difficult to predict an exact mode of SRO operation.3 In the linear
mode, the oscillation amplitude is measured before the oscillator reaches saturation,
providing a high independent gain.13
As depicted in the linear mode, the sampled envelope is much larger in the presence of
the RF input signal. Notice that, in this mode, the oscillator is disabled after the amplitude
is measured. Thus, in the linear mode, the oscillator never reaches saturation.
A logarithmic mode is described by a logarithmic relationship between the
amplitude of the RF input signal and the amplitude of the demodulated output
characterizes the logarithmic mode. In this mode the SRO reaches its steady-state
amplitude at each quench cycle, due to a low quench frequency and/or a high start-up
current; therefore, a reduction in the dynamic range of the demodulated output is due to
the logarithmic compression of the signal. In the logarithmic mode, however, the
oscillator is allowed to saturate during each cycle. The detector circuitry senses the area
under the oscillation envelope, providing a signal dependent gain.
As shown for the logarithmic mode, the area under the saturated oscillation
envelope is increased in the presence of an RF input, resulting from the decreased
oscillator start-up time in this condition. Due to severe fading anticipated in dense indoor
sensor networks, a very wide dynamic range is required from the receiver. The
logarithmic mode provides an inherent automatic gain control, making its use preferable
for this application.
Design Example
For validation purpose, a typical ISM band SRR at 433.92 MHz is taken for
design evaluation as described in the Design Basis, with the following specifications:
SRO O/P : 1V, Q0 of SN : 50, Q ≅ 5Q0 (assuming average Q is 5 times the quiescent Q
of the selective network), Gain of SN at resonance : 0 dB, Gain of LNA : 10 dB, RF O/P
of Antenna : -1 dBm, Bit rate: 10 kbps, RX modulation: OOK (ON-OFF Keying).8
From Equations 2 to 20, the design parameters can be evaluated as:
Oscillation frequency f0: 433.92 MHz. Modulation bandwidth: 10 kHz.
Quench frequency fq (fq ≅ 10 times modulation bandwidth): 100 kHz
Quiescent damping factor 2
0
0 1012
1: −×
Qς
Average damping factor 21022
1: −×=
Qdcς
SN gain K0 at resonance:0 dB
Regenerative gain dBdspKb
a
t
t
cr 30)()(: 00 ≅∫ τττως
Super regenerative gain dBeK
bt
d
s 40: 0
0 )(
≅∫− λλςω
Normalized envelope dBtpetp c
d
c
t
bt 17)(,:)(
)(0
−≅∫− λλςω
Peak gain dBKKKK sr 70: 0 ≅××
Effective gain dBtpKK ceff 53)(: ≅×
3dB bandwidth kHzf dB 4563 ≅∆
2.4 GHz SRR (Injection Mode-coupled SRO)
As depicted in the typical super-generative receiver circuit, the SRO module consists of
a lumped LC resonator network (Q ≅ 50 @ f = 2.4 GHz), which has a low Q and inherent
frequency instability due to temperature changes and mechanical shocks that can degrade
the accuracy and sensitivity of the SRR.
This problem can be overcome by means of a stable frequency reference, such as
high Q factor SAW/BAW resonator devices. However, SAW/BAW resonators are
expensive, sensitive to microphonics, and also not easily amenable to IC fabrication.
The circuit shown in Figure 12 responds to the above problem by making use of a
planar injection mode-coupled resonator, which improves the rate of change of phase and
group delay of the SRO, thereby improving sensitivity and dynamic ranges. This novel
configuration of SRO can be a cost-effective and power-efficient (3V, 6 mA) alternative
of SAW/BAW device SRR. The typical schematic shows the 2.4 GHz SRR using
injection mode-coupled SRO, where the printed mode-couple resonator network works as
a Q multiplier to support an optimum group delay during the active mode of operation (Q
≅ 412 @ f = 2.4 GHz), and the circuit is easily amenable for currently available IC
fabrication technology for mass commercial production.
Antenna
vRF(t)
Self-Injection Coupling
Mode-Coupled
De
tec
tor
Ou
tpu
t
LNA SRO
ED
NOISEFEEDBACKDC BIAS
Figure 12. Typical SRR using injection mode-coupled SRO.
From Equations 14 to 20, the performance parameters can be evaluated for comparative
analysis. The circuit is operated at a chip rate of 1.5 106 chips/sec for a sequence of 15
chip lengths, resulting a bit rate of 1 103 b/sec. Figure 13 depicts the typical SRO output
envelope. The overall sensitivity is calculated to be approximately 86 dB for a periodic
quench using a Gaussian chip envelope.
The drawbacks of injection mode-coupled SRR is frequency instability in planar
coupled resonator implementations, due to temperature variations. This problem can be
overcome by incorporating a phase locked loop (PLL) device (see Figure 14), thereby
improving performance and being easily amenable for currently available IC fabrication
technology for mass commercial productions. Additionally, a frequency synthesizer-based
approach is configurable for other operating frequency band; hence, a user defined SRR
module.
Figure 13. Typical CAD simulated SRO output envelope of the SRR.
PFDChargePump
Divider
fREF
gm(t)
LNA
An
ten
na
vRF(t)
RFin
LNA
Output
DSP
FrequencySynthesizer
Mode-Coupled Planar Resonator
Tuning Diode
ED
Quench Signal
Figure 14. A typical high sensitivity injection mode-coupled PLL based SRR
Conclusion
This article describes a planar injection mode-coupled SRR, which is a cost-
effective alternative to expensive high Q BAW/SAW resonator SROs for SRR
applications.
References
1 E.H. Armstrong, “Some Recent Developments of Regenerative Circuits,”
Proceedings of the IRE, Vol. 10, August 1922, pp. 244-260.
2 A. Vouilloz, M. Declercq and C. Dehollain, “A Low-power CMOS Super-
regenerative Receiver at 1 GHz,” IEEE Journal of Solid-State Circuits, Vol.
36, No. 3, March 2001, pp. 440-451.
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“ A 2 V 600 µA, 1 GHz BiCMOS Super-regenerative Receiver for ISM
Applications,” IEEE Journal of Solid State Circuits, Vol. 33, No. 12,
December 1998, pp. 2186-2196.
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403.
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Receiver,” IEEE Transactions on Consumer Electronics, May 1997, pp. 92-
102.
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IEEE Transactions on Circuits and Systems-I: Fundamental Theory and
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12 J. Whitehead, Super-regenerative Receivers, Cambridge Press, 1950.
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