Regenerative circuit

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Wikipedia

Homebuilt Armstrong one-tube regenerative shortwave radio with construction characteristic of the 1930s - 40s. The controls are (left) regeneration, (lower center) filament rheostat, (right) tuning capacitor.
Rear view of the above radio, showing the simplicity of the regenerative design. The tickler coil is visible inside the tuning coil and is turned by a shaft from the front panel; this type of adjustable transformer was called a variocoupler.

A regenerative circuit is an amplifier circuit that employs positive feedback (also known as regeneration or reaction).[1][2] Some of the output of the amplifying device is applied back to its input to add to the input signal, increasing the amplification.[3] One example is the Schmitt trigger (which is also known as a regenerative comparator), but the most common use of the term is in RF amplifiers, and especially regenerative receivers, to greatly increase the gain of a single amplifier stage.[4][5][6]

The regenerative receiver was invented in 1912[7] and patented in 1914[8] by American electrical engineer Edwin Armstrong when he was an undergraduate at Columbia University.[9]

The regenerative receiver was widely used from the mid-1910s through the 1920s, with use declining during the 1930s and becoming uncommon by the early 1940s.[10] Its principal advantage was high sensitivity with little added hardware, achieved by applying positive feedback around an RF detector stage and operating the circuit below the onset of oscillation.

Armstrong’s key insight was that radio-frequency energy existed in the detector’s plate circuit and could be fed back to the input, contrary to the prevailing belief that only audio frequencies remained after detection.[11] When carefully adjusted, this feedback greatly increased the effective gain of a single active device, though operating required skill.

Regeneration improves selectivity by increasing loop gain near resonance, sharpening the frequency response without altering the intrinsic Q of the tuned circuit itself. The effect is equivalent to compensating circuit losses through feedback, simulating a negative resistance. As noted by Terman, regenerative detectors suffer from excessive selectivity, frequency-dependent critical adjustment, and a tendency toward oscillation that can produce interference and audible whistles if regeneration is increased too far.[10] With the development of radio-frequency amplifiers designed around better tubes, regenerative detectors found relatively little application after the early 1930s.[10]

A receiver circuit that used larger amounts of regeneration in a more complicated way to achieve even higher amplification, the superregenerative receiver, was also invented by Armstrong in 1922.[12][5]: p.190  It was never widely used in general commercial receivers, but due to its small parts count it was used in specialized applications. One widespread use during WWII was IFF transceivers, where single tuned circuit completed the entire electronics system. It is still used in a few specialized low data rate applications,[12] such as garage door openers,[13] wireless networking devices,[12] walkie-talkies and toys.

Regenerative receiver

Vacuum tube regenerative receiver schematic. Most regenerative receivers used this Armstrong circuit, in which the feedback was applied to the input (grid) of the tube with a "tickler coil" winding on the tuning inductor.

In a regenerative receiver, a portion of the detector’s RF output is fed back to its input through a tuned circuit, providing frequency-selective positive feedback. When adjusted below oscillation, this feedback substantially increases sensitivity and selectivity, allowing RF amplification and detection to be implemented using a single active device.[14][3][15][16][17]

Regeneration sharpens the receiver’s frequency response by increasing loop gain near resonance. The intrinsic Q of the tuned circuit itself is unchanged; instead, feedback compensates for circuit losses, producing behavior mathematically equivalent to reducing resistive loss. As the loop gain approaches unity, the effective bandwidth narrows rapidly. Oscillation begins when losses are fully compensated.[16][3]

Contemporary measurements showed that regeneration could increase detector gain by orders of magnitude. For example, a type 36 screen-grid tube with a non-regenerative detection gain of about 9 at 7.2 MHz achieved gains exceeding 7,000 under critical regeneration, with higher values possible near oscillation.[17]

A major improvement in stability and a small improvement in available gain for reception of CW radiotelegraphy is provided by the use of a separate oscillator, known as a heterodyne oscillator or beat oscillator.[17][18] Providing the oscillation separately from the detector allows the regenerative detector to be set for maximum gain and selectivity - which is always in the non-oscillating condition.[17][19] Interaction between the detector and the beat oscillator can be minimized by operating the beat oscillator at half of the receiver operating frequency, using the second harmonic of the beat oscillator in the detector.[18]

AM reception

For AM reception, the gain of the loop is adjusted so it is just below the level required for oscillation (a loop gain of just less than one). The result of this is to greatly increase the gain of the amplifier at the bandpass frequency (resonant frequency), while not increasing it at other frequencies. So the incoming radio signal is amplified by a large factor, 103 - 105, increasing the receiver's sensitivity to weak signals. The high gain also has the effect of reducing the circuit's bandwidth (increasing the Q) by an equal factor, increasing the selectivity of the receiver.[20]

CW reception (autodyne mode)

For the reception of CW radiotelegraphy (Morse code), the feedback is increased just to the point of oscillation. The tuned circuit is adjusted to provide typically 400 to 1000 Hertz difference between the receiver oscillation frequency and the desired transmitting station's signal frequency. The two frequencies beat in the nonlinear amplifier, generating heterodyne or beat frequencies.[21] The difference frequency, typically 400 to 1000 Hertz, is in the audio range; so it is heard as a tone in the receiver's speaker whenever the station's signal is present.

Demodulation of a signal in this manner, by use of a single amplifying device as oscillator and mixer simultaneously, is known as autodyne reception.[22] The term autodyne predates multigrid tubes and is not applied to use of tubes specifically designed for frequency conversion.

SSB reception

For the reception of single-sideband (SSB) signals, the circuit is also adjusted to oscillate as in CW reception. The tuning is adjusted until the demodulated voice is intelligible.

Advantages and disadvantages

Regenerative receivers require fewer components than other types of receiver circuit, such as the TRF and superheterodyne. The circuit's advantage was that it got much more amplification (gain) out of the expensive vacuum tubes, thus reducing the number of tubes required and therefore the cost of a receiver. Early vacuum tubes had low gain and tended to oscillate at radio frequencies (RF). TRF receivers often required 5 or 6 tubes; each stage requiring tuning and neutralization, making the receiver cumbersome, power hungry, and hard to adjust. A regenerative receiver, by contrast, could often provide adequate reception with the use of only one tube. In the 1930s the regenerative receiver was replaced by the superheterodyne circuit in commercial receivers due to the superheterodyne's superior performance and the falling cost of tubes. Since the advent of the transistor in 1946, the low cost of active devices has removed most of the advantage of the circuit. However, in recent years the regenerative circuit has seen a modest comeback in receivers for low cost digital radio applications such as garage door openers, keyless locks, RFID readers and some cell phone receivers.

A disadvantage of this receiver, especially in designs that couple the detector tuned circuit to the antenna, is that the regeneration (feedback) level must be adjusted when the receiver is tuned to a different frequency. The antenna impedance varies with frequency, changing the loading of the input tuned circuit by the antenna, requiring the regeneration to be adjusted. In addition, the Q of the detector tuned circuit components vary with frequency, requiring adjustment of the regeneration control.[5]: p.189 

A disadvantage of the single active device regenerative detector in autodyne operation is that the local oscillation causes the operating point to move significantly away from the ideal operating point, resulting in the detection gain being reduced.[19]

Another drawback is that when the circuit is adjusted to oscillate it can radiate a signal from its antenna, so it can cause interference to other nearby receivers. Adding an RF amplifier stage between the antenna and the regenerative detector can reduce unwanted radiation, but would add expense and complexity.

Other shortcomings of regenerative receivers are the sensitive and unstable tuning. These problems have the same cause: a regenerative receiver's gain is greatest when it operates on the verge of oscillation, and in that condition, the circuit behaves chaotically.[23][24][25] Simple regenerative receivers electrically couple the antenna to the detector tuned circuit, resulting in the electrical characteristics of the antenna influencing the resonant frequency of the detector tuned circuit. Any movement of the antenna or large objects near the antenna can change the tuning of the detector.

History

1915 Armstrong regenerative receiver

The inventor of FM radio, Edwin Armstrong, filed US patent 1113149 in 1913 about regenerative circuit while he was a junior in college.[26] He patented the superregenerative circuit in 1922, and the superheterodyne receiver in 1918.

Lee De Forest filed US patent 1170881 in 1914 that became the cause of a contentious lawsuit with Armstrong, whose patent for the regenerative circuit had been issued in 1914. The lawsuit lasted until 1934, winding its way through the appeals process and ending up at the Supreme Court. Armstrong won the first case, lost the second, stalemated at the third, and then lost the final round at the Supreme Court.[27][28]

At the time the regenerative receiver was introduced, vacuum tubes were expensive and consumed much power, with the added expense and encumbrance of heavy batteries. So this design, getting most gain out of one tube, filled the needs of the growing radio community and immediately thrived. Although the superheterodyne receiver is widely used today[29], the regenerative radio made the most out of very few parts.

In World War II the regenerative circuit was used in some military equipment. An example is the German field radio "Torn.E.b".[30] Regenerative receivers needed far fewer tubes and less power consumption for nearly equivalent performance.

A related circuit, the superregenerative detector, found several highly important military uses in World War II in Friend or Foe identification equipment]. An example here is the miniature RK61 thyratron marketed in 1938, which was designed specifically to operate like a vacuum triode below its ignition voltage, allowing it to amplify analog signals as a self-quenching superregenerative detector in radio control receivers,[31] and was the major technical development which led to the wartime development of radio-controlled weapons and the parallel development of radio controlled modelling as a hobby.[32]

In the 1930s, the superheterodyne design began to gradually supplant the regenerative receiver, as tubes became far less expensive. In Germany the design was still used in the millions of mass-produced German "peoples receivers" (Volksempfänger) and "German small receivers" (DKE, Deutscher Kleinempfänger). Even after WWII, the regenerative design was still present in early after-war German minimal designs along the lines of the "peoples receivers" and "small receivers", dictated by lack of materials. Frequently German military tubes like the "RV12P2000" were employed in such designs. There were even superheterodyne designs, which used the regenerative receiver as a combined IF and demodulator with fixed regeneration. The superregenerative design was also present in early FM broadcast receivers around 1950. Later it was almost completely phased out of mass production, remaining only in hobby kits, and some special applications, like gate openers.

Superregenerative receiver

Edwin Armstrong presenting the superregenerative receiver at the June 28, 1922 meeting of the Radio Club of America in Havemeyer Hall, Columbia University, New York. His prototype 3 tube receiver was as sensitive as conventional receivers with 9 tubes.

A superregenerative receiver is a radio receiver that achieves high sensitivity by periodically varying the stability of a resonant circuit. Edwin H. Armstrong introduced the technique in 1922 as an extension of the regenerative receiver. The circuit repeatedly drives a tuned stage above and below the threshold of oscillation. During each cycle, signals grow exponentially while the circuit is unstable and decay when stability returns. This process enables the detection of very weak radio signals with effective gains approaching 120 dB, while using relatively simple circuitry and low power.

Engineers studied superregenerative receivers extensively in the 1930s and deployed them widely during the Second World War. They formed the receiving element in identification friend or foe (IFF) systems that identified friendly aircraft and ships, and in beacon systems such as Rebecca–Eureka that helped aircraft locate ground positions in flight. Large-scale wartime production showed that manufacturers could engineer the design for consistent performance.

After the war, designers adopted superregenerative circuits for low-cost and battery-powered applications including hobby radio control systems, garage door openers, and wireless doorbells. Although more complex receiver architectures later dominated most communication systems, superregenerative techniques continue to attract research interest. Recent work includes updated theoretical analyses and implementations at millimeter-wave frequencies. Their combination of high sensitivity, circuit simplicity, and energy efficiency has maintained their relevance in specialized and short-range applications.

History

Origin and early development

The superregenerative receiver was introduced in 1922 by Edwin H. Armstrong as an extension of the regenerative receiver.[33][34] In that paper, Armstrong described a method in which a regenerative detector was periodically driven into and out of oscillation by a quench signal, producing repeated cycles of oscillation build-up and decay. Because the amplification obtained exceeded what had previously been considered the theoretical limit of regenerative amplification, Armstrong referred to the process as “super-regeneration.”[33]

Further theoretical analysis appeared during the 1930s. In 1938, F. W. Frink published a detailed treatment in the Proceedings of the IRE that distinguished between linear and logarithmic modes of operation and compared analytical results with laboratory measurements.[35]

Superregenerative and regenerative techniques were also explored for portable communication. A 1936 article in Wireless Engineer described a 20-pound portable duplex radio telephone using super-regenerative circuitry that functioned alternately as receiver and transmitter.[36] The system reportedly operated in full duplex over short ranges, with oscillators at each end synchronizing when properly tuned.

WWII airborn component of the Rebecca-Eureka beacon system. Used in the Normandy invasion.

Wartime applications

Superregenerative receivers saw extensive use during the Second World War, particularly in identification friend or foe (IFF) systems. They were employed in IFF Mark III airborne responders used by Allied forces.[37] More than 200,000 such units were produced in the United Kingdom and the United States, with production tolerances reportedly maintained within 5 dB over a 30 MHz band.[38]

Superregenerative receivers formed the “Eureka” portion of the Rebecca–Eureka radar navigation system and related interrogation-response arrangements. These systems assisted aircraft in locating ground beacons during airborne operations, including those conducted during the Second World War.[39][40]

Large-scale wartime production indicated that superregenerative receivers could be engineered for stable and reproducible performance, addressing earlier concerns about variability.[38]

Postwar consumer and hobby use

After the war, superregenerative receivers became widely used in low-cost consumer and hobby applications. A June 1947 issue of Electronics magazine described a single-tube superregenerative receiver using a thyratron for hobby radio-control systems.[41] Raytheon also published a circuit combining a tube and a transistor.[42] The simplicity and high sensitivity of the design made it attractive for inexpensive remote-control equipment.

Superregenerative receivers were subsequently adopted in short-range consumer devices such as garage door openers, wireless doorbells, and radio-controlled toys. Their low component count, low power consumption, and adequate selectivity for narrowband applications contributed to widespread use in these products.[43]

Postwar theoretical development

In 1946, Wireless World reassessed the main criticisms of superregenerative receivers and clarified the distinction between linear and logarithmic modes of operation. In logarithmic mode, oscillations reach their limiting amplitude during each quench cycle, producing very high amplification but also distortion and automatic gain effects. In linear mode, oscillations are quenched before full build up, producing output proportional to the input and making the technique suitable for pulse detection applications such as IFF. The article also described the use of contemporary multi grid valves, including octodes, to combine quench and radio frequency functions within a single device.[44]

In 1949, Herbert A. Glucksmann published an analysis of the linear mode in the Proceedings of the IRE, modeling the superregenerative receiver as a tuned circuit with periodically varying damping.[45] His work examined frequency response characteristics and contributed to a more formal theoretical framework.

In 1950, J. R. Whitehead published one of the first comprehensive books devoted entirely to superregenerative receivers, summarizing both theoretical developments and wartime engineering practice.[46]

Ongoing research and modern applications

Superregenerative techniques have continued to attract research interest into the 21st century. Recent IEEE publications have examined both modern linear-mode implementations and operation at millimeter-wave frequencies[47], including work investigating super-regenerative reception at 100 GHz.[48]

Unintended emissions from superregenerative receivers have also been studied as identifiable device signatures. A 2013 paper in the IEEE Transactions on Instrumentation and Measurement demonstrated detection of superregenerative receivers used in devices such as garage door openers and wireless doorbells by analyzing statistical properties of their emissions.[43]

Principles of operation

A circuit diagram from the Armstrong 1922 patent. Triode 23 is the detector. Triode 29 is the quench oscillator. The quench oscillator varies the plate voltage available to 23.

A superregenerative receiver operates by periodically varying the effective damping of a resonant circuit so that it alternates between unstable and stable conditions.[33] During part of each quench cycle the circuit exhibits negative effective damping, causing oscillations to grow exponentially. During the remainder of the cycle the damping becomes positive and the oscillations decay exponentially. This alternation is controlled either by a separate quench oscillator or by internal circuit dynamics.[49]

Effective negative resistance

With appropriate positive feedback, the active device in the receiver behaves as a negative resistance at the resonant frequency.[33] When the magnitude of this negative resistance exceeds the losses of the tuned circuit, the net damping becomes negative and oscillations increase exponentially. When the net resistance becomes positive again, oscillations decay. The negative resistance is normally modulated by varying the gain of the active device.[50]

Armstrong noted that the alternating growth and decay required for superregeneration could be produced by varying the negative resistance component, the positive resistance component, or both.[33]

Quench and signal operations from the 1922 Armstrong paper. The R tube is the receiving tube. The O tube is the quench oscillator.

Exponential growth and effective gain

When the circuit is in its unstable region, oscillations grow exponentially from the instantaneous signal level or from internal noise.[35] Because exponential growth can produce large amplitude increases over short time intervals, the effective gain during the growth phase can approach 106 (approximately 120 dB), depending on circuit parameters and quench timing.[51]

This repeated process of exponential growth and suppression was termed “super-regeneration” by Armstrong to distinguish it from ordinary regenerative amplification.[33][52]

Modes of operation

The behavior of the receiver depends on how long the circuit remains in the unstable region during each quench cycle.[35][53]

Linear mode

In linear mode, the circuit is returned to the stable region before oscillation reaches its steady-state limiting amplitude. The peak oscillation amplitude remains approximately proportional to the input signal amplitude. To maintain proportional operation, automatic gain stabilization techniques are generally required to prevent the circuit from drifting into limiting behavior.[54]

Logarithmic (nonlinear) mode

If the circuit remains in the unstable region long enough for oscillation to reach its steady-state limiting amplitude during each cycle, the output depends primarily on the time required for oscillation to reach saturation. This produces an approximately logarithmic relationship between input and output signal strength and provides large dynamic range.[55]

Self quenching circuit from US 2,644,080.

Self-quenching (single-device) mode

In some implementations, a separate quench oscillator is not used. Instead, internal bias changes within the active device generate a low-frequency oscillation that periodically drives the high-frequency oscillation above and below the instability threshold. In this case the circuit operates as two coupled oscillatory processes: a high-frequency RF oscillation and a lower-frequency quench oscillation. The resulting response is also logarithmic in character, since the RF oscillation typically reaches its limiting amplitude during each burst.[56]

Time-varying system analysis

Later theoretical treatments modeled the superregenerative receiver as a resonant circuit with periodically varying damping.[57] In this formulation the receiver is described as a linear time-varying (LTV) system rather than a linear time-invariant (LTI) system. This approach provided a formal framework for analyzing oscillation growth, bandwidth, and frequency response in linear mode, and clarified the relationship between quench frequency and receiver performance.[57]

Sub-sampling

The periodic quench process causes the receiver to restart detection at a fixed interval. In The Design and Implementation of Low-Power CMOS Radio Receivers, Shaeffer and Lee describe the superregenerative receiver as the first sub-sampled radio architecture.[58]

Radiation of unintended/intended emissions

Because the circuit periodically enters an oscillatory state, some radiation may occur from the antenna or associated circuitry during the growth intervals. This characteristic has influenced practical circuit design, shielding, and regulatory considerations.  In IFF implementations, controlled radiation was intentionally used as part of the interrogation–response mechanism, with circuit bias adjusted to produce a retransmitted signal.[59]

Chaotic behavior

Whitehead noted that oscillations from one quench cycle must decay before the next begins, otherwise subsequent cycles will build upon residual oscillations rather than the input signal.[60]

Later studies have examined operating regimes in which superregenerative detectors exhibit chaotic behavior under certain quench-to-radio-frequency ratios and gain conditions.[61][62]

Patents

  • US 1113149, Armstrong, E. H., "Wireless receiving system", published Oct. 6, 1914, issued Oct. 29, 1913 
  • US 1170881, de Forest, Lee, "Wireless receiving system", published Feb. 8, 1916, issued Mar. 12, 1914 
  • US 1342885, Armstrong, E. H., "Method of receiving high frequency oscillation", published February 8, 1919, issued June 8, 1920 
  • US 1424065, Armstrong, E. H., "Signalling system", published June 27, 1921, issued July 25, 1922 
  • US 2211091, Braden, R. A., "Superregenerative magnetron receiver"  1940.

See also

References

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  2. ↑ E. Williams, Thermionic Valve Circuits, 4th ed., London: Sir Isacc Pitman & Sons, 1961, p. 151
  3. 1 2 3 Everitt, W. L. (William Littell) (1937). Communication engineering. Internet Archive. New York, London, McGraw-Hill Book Co.
  4. ↑ J. Scott-Taggart, The Manual of Modern Radio, London: The Amalgamated Press LTD., 1933, p. 94
  5. 1 2 3 Technical Manual TM 11-665: C-W and A-M Radio Transmitters and Receivers. Dept. of the Army, US Government Printing Office. 1952. pp. 187–190.
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  7. ↑ Hong, Sungook. "A history of the regeneration circuit: From invention to patent litigation" (PDF). Institute of Electrical and Electronics Engineers. Retrieved March 9, 2014.
  8. ↑ US Patent 1113149A, Edwin H. Armstrong, Wireless receiving system, filed October 29, 1913, granted October 6, 1914
  9. ↑ Armstrong, Edwin H. (September 1915). "Some recent developments in the Audion receiver" (PDF). Proc. IRE. 3 (9). New York: Institute of Radio Engineers: 215–247. doi:10.1109/JRPROC.1915.216677. S2CID 2116636. Archived from the original (PDF) on July 28, 2013. Retrieved August 29, 2012.
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  25. ↑ In 1922, during his development of the superregenerative receiver, Edwin Armstrong noted signs of chaotic behavior in his circuits. See: Edwin H. Armstrong (1922) "Some recent developments of regenerative circuits," Proceedings of the Institute of Radio Engineers, 10 (8) : 244-260. From p. 252: " ... a free oscillation starts every time the resistance of the circuit becomes negative. ... The free oscillations produced in the system when no signaling emf. is impressed, must be initiated by some irregularity of operation of the vacuum tubes, ... ."
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  33. 1 2 3 4 5 6 Armstrong, E.H. (August 1922). "Some Recent Developments of Regenerative Circuits". Proceedings of the IRE. 10 (4): 244–260. doi:10.1109/JRPROC.1922.219822. ISSN 0096-8390.
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  35. 1 2 3 Frink, F.W. (January 1938). "The Basic Principles of Super-Regenerative Reception". Proceedings of the IRE. 26 (1): 76–106. doi:10.1109/JRPROC.1938.228669. ISSN 0096-8390.
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  48. ↑ Feng, Guangyin; Boon, Chirn Chye; Meng, Fanyi; Yi, Xiang (July 2016). "A 100-GHz 0.21-K NETD 0.9-mW/pixel Charge-Accumulation Super-Regenerative Receiver in 65-nm CMOS". IEEE Microwave and Wireless Components Letters. 26 (7): 531–533. doi:10.1109/LMWC.2016.2574833. ISSN 1531-1309.
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  55. ↑ Whitehead, J. R. (1950). Super-Regenerative Receivers (PDF). Cambridge University Press. pp. 100–110.
  56. ↑ Whitehead, J. R. (1950). Super-Regenerative Receivers (PDF). Cambridge University Press. pp. 111–115.
  57. 1 2 Glucksmann, H. A. (May 1949). "Superregeneration—An Analysis of the Linear Mode". Proceedings of the IRE. 37 (5): 500–504. doi:10.1109/JRPROC.1949.232646.
  58. ↑ Shaeffer, Derek K.; Lee, Thomas H. (1999). The Design and Implementation of Low-Power CMOS Radio Receivers. Kluwer Academic. pp. 9–11.
  59. ↑ Whitehead, J. R. (1950). Super-Regenerative Receivers (PDF). Cambridge University Press. pp. 144–149.
  60. ↑ Whitehead, J. R. (1950). Super-Regenerative Receivers (PDF). Cambridge University Press. p. 1.
  61. ↑ Domine M.W. Leenaerts and Wim M.G. van Bokhoven, “Amplification via chaos in regenerative detectors,” Proceedings of SPIE, vol. 2612, 1995, pp. 136–145.
  62. ↑ Domine M.W. Leenaerts, “Chaotic behavior in superregenerative detectors,” IEEE Transactions on Circuits and Systems I, vol. 43, no. 3, 1996, pp. 169–176.
  • Lewis, Tom (1991), Empire of the Air: the men who made radio, New York: Edward Burlingame Books, ISBN 0060981199
  • Morse, A. H. (1925), Radio: Beam and Broadcast, London: Ernest Benn Limited. History of radio in 1925. Has May 5, 1924, appellate decision by Josiah Alexander Van Orsdel in De Forest v Armstrong, pp 46–55. Appellate court credited De Forest with the regenerative circuit: "The decisions of the Commissioner are reversed and priority awarded to De Forest." p 55.
  • Robinson, H. A. (February 1933), "Regenerative Detectors, What We Get From Them - How To Get More", QST, 17 (2): 26–30 & 90
  • Ulrich L. Rohde, Ajay Poddar www.researchgate.net/publication/4317999_A_Unifying_Theory_and_Characterization_of_Super-Regenerative_Receiver_(SRR)