1

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.

3 P. Favre, N. Joehl, A. Vouilloz, P. Deval, C. Dehollain and M.J. Declercq,

“ 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.

4 N.B. Buchanan, V.F. Fusco and J.A.C. Steward, “A Ka-band MMIC Super-

regenerative Detector,” 2000 IEEE MTT-S International Microwave

Symposium Digest, Vol. 3, pp. 1585-1558.

5 W.G. McCoy, “Design of a Super-regenerative Receiver for Solar Powered

Applications,” IEEE Transactions on Consumer Electronics, Vol. 38,

November 1992, pp. 869-873.

6 D.L. Ash, “A Low Cost Superregenerative SAW Stabilized Receiver,”

IEEE Transactions on Consumer Electronics, Vol. 3, Aug. 1987, pp. 395-

403.

7 N. Joehl, C. Dehollain, P. Favre, P. Deval and M. Declercq, “A Low-power

1 GHz Super-regenerative Transreceiver with Time-shared PLL Control,”

IEEE Journal of Solid State Circuits, Vol. 36, No. 7, July 2001, pp. 1025-

1031.

8 F.X. Moncunill, P. P-Schonwalder and O.M-Casals, “A Generic Approach

to the Theory of Super-regenerative Reception,” IEEE Transactions on

Circuit and Systems-I, Vol. 52, January 2005, pp. 54-70.

9 R. Feick and O. Rojas, “Modeling and Simulation of the Super-regenerative

Receiver,” IEEE Transactions on Consumer Electronics, May 1997, pp. 92-

102.

10 D.M.W. Leenaerts, “Chaotic Behavior in Superregenerative Detectors,”

IEEE Transactions on Circuits and Systems-I: Fundamental Theory and

Applications, Vol. 43, March 1996, pp. 169-176.

11 A. Jamet, “A 10 GHz Super-regenerative Receiver,” VHF Communications,

Vol. 29, K.M. Publications, UK, 1997, pp. 2-12.

12 J. Whitehead, Super-regenerative Receivers, Cambridge Press, 1950.

13 B.P. Otis, “Ultra-low Power Wireless Technologies for Sensor Networks,”

Thesis, University of California, Berkeley, February 2005.