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Continuous wave

A continuous wave (CW) is a waveform characterized by constant amplitude and frequency, resulting in a steady power output over time without interruptions or pulses.^[1] This contrasts with pulsed waves, where energy is emitted in discrete bursts, allowing CW signals to maintain a continuous sinusoidal oscillation suitable for various transmission and detection applications. The development of continuous wave technology marked a pivotal advancement in radio communication during the early 20th century. In 1906, Reginald Fessenden achieved the first successful CW transmission using a high-frequency alternator transmitter at his Brant Rock station in Massachusetts, enabling voice and music broadcasts over long distances and surpassing the limitations of earlier spark-gap systems that produced damped waves.^[2] This innovation laid the foundation for modern radiotelegraphy and telephony, with widespread adoption by amateurs and professionals by the 1920s, as CW proved more efficient for Morse code signaling and spectrum utilization.^[3] CW finds extensive use across electromagnetics, optics, and acoustics due to its stable output. In radio and radar systems, CW enables precise Doppler shift measurements for velocity detection, as the continuous transmission allows simultaneous reception of reflected signals to compute frequency changes caused by moving targets.^[4] In lasers, CW operation provides uninterrupted light emission for applications like precision welding, cutting, and alignment in manufacturing, where constant power ensures smooth material processing without thermal damage from pulses.^[5] Additionally, in medical ultrasound and spectroscopy, CW techniques facilitate real-time flow monitoring and tissue analysis by injecting steady waves to detect attenuation or shifts without range ambiguity issues common in pulsed methods.^[6]

Fundamentals

Definition and Properties

A continuous wave (CW) is an electromagnetic wave characterized by a constant power output over time, typically manifesting as a sinusoidal oscillation with unchanging amplitude and frequency, in distinction from modulated signals that vary in amplitude, frequency, or phase to convey information, or pulsed signals that are intermittently transmitted.^[1] This steady emission ensures the wave propagates without interruptions, maintaining a consistent carrier signal suitable for applications requiring stable transmission.^[1] Key properties of a continuous wave include its fixed carrier frequency, constant amplitude, and unbroken phase continuity, which collectively result in a pure, undamped sinusoidal form devoid of transient variations.^[1] The energy density of the electric field component in vacuum is expressed as u_E = \frac{1}{2} \epsilon_0 E^2, where \epsilon_0 is the vacuum permittivity and E is the instantaneous electric field strength; the total electromagnetic energy density combines this with the magnetic field contribution, u_B = \frac{B^2}{2 \mu_0}, yielding u = \epsilon_0 E^2 for plane waves where the electric and magnetic energies are equal.^[7] Mathematically, a continuous wave is represented as y(t) = A \cos(2\pi f t + \phi), where A denotes the constant amplitude, f the fixed frequency, t time, and \phi the initial phase; in the frequency domain, its power spectral density is a Dirac delta function centered at f, reflecting the monochromatic nature of the signal.^[8] The wavelength \lambda of a continuous wave relates inversely to its frequency via \lambda = \frac{[c](/page/Speed_of_light)}{[f](/page/Frequency)}, with c being the speed of light in vacuum ($3 \times 10^8 m/s), allowing waves to span vast scales from meters in radio bands to micrometers in infrared. Continuous waves operate across frequencies from kilohertz (kHz) in very low-frequency radio communications to terahertz (THz) in advanced imaging and sensing, adapting to diverse propagation and interaction characteristics in each regime.

Generation and Detection

In the radio and microwave regimes, continuous wave (CW) signals are generated using electronic oscillators that produce a stable sinusoidal waveform at a fixed frequency.^[11] Early generation methods relied on vacuum tube oscillators, where a high-vacuum tube served as the active device to sustain oscillations and generate continuous waves, particularly at higher frequencies.^[12] In modern systems, solid-state devices such as transistors have largely replaced vacuum tubes, forming the basis of oscillators like the Colpitts configuration, which uses a transistor for amplification and feedback to produce clean sine waves suitable for CW transmission.^[13] Crystal oscillators, employing quartz crystals via the piezoelectric effect, provide exceptional frequency stability by replacing less precise LC tank circuits, achieving Q-factors of 20,000 to 200,000 that minimize drift from environmental factors.^[14] Following oscillation, the signal is amplified using power amplifiers to reach desired output levels, ensuring sufficient strength for transmission without distortion.^[13] Typical CW transmitters include simple LC oscillators for basic applications, where an inductor-capacitor network sets the resonant frequency, though these suffer from lower stability compared to crystal-based designs.^[14] More advanced transmitters incorporate Pierce crystal oscillators, utilizing a transistor (e.g., JFET) with the quartz crystal in the feedback path to generate stable signals in the range of 40 kHz to over 100 MHz, ideal for precise communication and sensing.^[14] Detection of CW signals primarily involves coherent techniques for phase-sensitive measurement, where the incoming signal is mixed with a local oscillator (LO) in a mixer to downconvert it while preserving amplitude and phase information, often using a photodiode or electronic mixer for enhanced sensitivity.^[15] Envelope detectors, consisting of a diode for rectification followed by a low-pass RC filter, can recover amplitude variations in CW signals, though they are less common for unmodulated carriers and more suited to amplitude-modulated contexts.^[16] Superheterodyne receivers tune to the carrier frequency by adjusting the LO to produce a fixed intermediate frequency (IF), typically 30–75 MHz, allowing subsequent amplification and demodulation of the CW signal.^[17] Receivers for CW signals often employ bandpass filters to isolate the narrowband carrier from broadband noise and interference, enabling effective detection even in noisy environments. Key challenges in CW generation and detection include maintaining frequency stability, addressed by quartz crystals that limit deviations to ±20–100 ppm over temperature ranges like -40°C to +85°C, with aging drift as low as ±3 ppm in the first year for high-quality units.^[18] Short-term drift rates can be controlled below 1 Hz over seconds in stabilized oscillators, preventing signal misalignment.^[18] Signal-to-noise ratio (SNR) improvements are achieved through narrowband filtering, which rejects out-of-band noise while passing the CW signal's limited bandwidth, potentially boosting SNR by several dB in optical or RF systems.

Historical Development

Pre-CW Transmissions

Early radio transmissions relied on spark-gap transmitters, which produced damped electromagnetic waves through the discharge of electrical sparks across a gap. In 1887, Heinrich Hertz demonstrated the existence of radio waves using a spark-gap setup to generate and detect oscillations, confirming James Clerk Maxwell's theoretical predictions. Building on this, Guglielmo Marconi developed practical wireless telegraphy in the 1890s, employing spark transmitters with monopole antennas to send Morse code signals over distances, achieving transatlantic communication by 1901.^[19]^[20] To overcome the limitations of damped waves, inventors explored undamped signal generation using arc transmitters and high-frequency alternators, though these early methods remained inefficient. Arc transmitters, pioneered by Valdemar Poulsen around 1902, utilized a sustained electric arc between carbon electrodes to produce continuous oscillations, enabling more stable but power-hungry signals suitable for telephony experiments.^[19] Meanwhile, Ernst Alexanderson designed high-frequency alternators starting in 1904 at General Electric, which mechanically generated sinusoidal waves via rotating armatures, with early models outputting up to 2 kW at 100 kHz.^[21] Larger Alexanderson alternators later achieved powers of 10 to 200 kW at low frequencies between 10 and 100 kHz, primarily for long-wave applications.^[22] Pre-CW transmissions, particularly from spark-gap devices, exhibited broad spectral characteristics due to their transient, noise-like pulses, occupying wide bandwidths and causing significant interference among stations. These damped waves consisted of rapidly decaying oscillations, making precise tuning difficult as receivers struggled to filter signals without a steady carrier for synchronization. Arc and alternator systems offered narrower spectra with undamped outputs but suffered from low efficiency, high mechanical complexity, and limited frequency control, restricting their scalability.^[23]^[24] In the early 1900s, spark-gap transmitters saw widespread adoption in maritime and military communications for their simplicity and reliability in distress signaling. By 1904, the Royal Navy equipped ships with wireless sets using spark technology, enabling coordination during maneuvers and battles, such as the Russo-Japanese War where Japanese vessels demonstrated its tactical value. These systems facilitated ship-to-shore and inter-ship messaging but were plagued by mutual interference in congested areas, underscoring the need for spectrum-efficient alternatives.^[25]^[26] A notable CW milestone occurred in 1906 when Reginald Fessenden used an Alexanderson alternator to transmit the first voice and music broadcasts from Brant Rock, Massachusetts, on December 24, demonstrating the potential of continuous carriers for amplitude modulation despite the technology's inefficiencies.^[20]^[27]

Transition to CW

The transition from damped spark transmissions to continuous wave (CW) radio began with early experiments in the late 1900s, driven by the need to overcome the limitations of spark systems, which produced broad, noisy signals prone to interference. In 1906, Reginald Fessenden achieved the first successful CW transmission using a high-frequency alternator, marking a foundational step toward stable, undamped signals suitable for both telegraphy and voice.^[19] This innovation laid the groundwork for subsequent developments, though widespread adoption required further technological and regulatory advancements. Key inventions accelerated the shift. Lee de Forest's 1906 audion tube, a triode vacuum tube, enabled amplification and laid the basis for vacuum-tube oscillators essential to CW generation.^[28] In 1913, Edwin Howard Armstrong patented the regenerative feedback circuit, which provided stable oscillation for reliable CW transmitters by feeding a portion of the output signal back to the input, dramatically improving signal purity and efficiency.^[29] These vacuum-tube technologies supplanted earlier mechanical methods like Fessenden's alternators and Poulsen's arcs, offering compact, scalable solutions for commercial and maritime use.^[30] The 1912 sinking of the RMS Titanic, where spark transmitters' interference hampered distress signals, underscored the urgency for clearer communication and hastened regulatory reforms.^[31] In response, the International Radiotelegraph Convention of 1912 mandated improved radio practices for ships, including continuous monitoring and standardized equipment that favored CW for its reliability in emergencies.^[30] Concurrently, the U.S. Radio Act of 1912 prohibited inefficient spark transmitters on large vessels over 300 gross tons, requiring CW-capable systems to enhance safety and reduce interference.^[30] CW's technical superiority fueled its adoption: unlike spark transmissions, which occupied tens of kilohertz due to damped oscillations spreading energy across multiple frequencies, CW signals maintained a narrow bandwidth under 1 kHz, enabling sharper selectivity, longer range, and minimal interference.^[32] This efficiency proved vital for maritime and transoceanic links, with CW circuits spanning thousands of miles by the late 1910s. By the 1920s, CW had become dominant, outnumbering spark stations two-to-one by 1920 and achieving near-universal use in professional radio.^[19] Amateur radio operators embraced CW alongside innovations like superregenerative receivers, invented by Armstrong in 1922, which offered high sensitivity for detecting faint CW signals and proliferated in hobbyist sets throughout the decade.^[33]

Persistence of Telegraphy

Despite the advent of amplitude modulation (AM) and frequency modulation (FM) technologies in the early 20th century, continuous wave (CW) telegraphy persisted due to its inherent simplicity, requiring only basic on-off keying of a carrier signal without complex modulation circuits. This minimalism made CW reliable in adverse conditions, such as during World War II and subsequent conflicts, where it served aviation and military communications for precise, low-bandwidth messaging until the 1990s, when satellite and digital systems began supplanting it. Additionally, CW's low power requirements enabled global reach with modest equipment; for instance, 5 watts of CW power could achieve distances comparable to 100 watts of voice transmission, conserving resources in remote or emergency scenarios.^[34]^[35]^[36] In niche applications, CW telegraphy found enduring roles among amateur radio operators, particularly in Morse code contests organized by bodies like the American Radio Relay League (ARRL), which host events such as the ARRL DX CW Contest to hone operating skills and test propagation. It also underpinned international distress signaling until the Global Maritime Distress and Safety System (GMDSS) fully phased out Morse code on February 1, 1999, replacing manual telegraphy with automated digital alerts for enhanced maritime safety. Furthermore, CW beacon stations, coordinated through projects like the International Beacon Project (IBP), continue to transmit Morse identifications on HF bands to monitor ionospheric propagation conditions, aiding both amateur and professional radio users in predicting signal paths.^[37]^[38]^[39] The decline of CW telegraphy accelerated post-World War II as commercial broadcasting shifted to voice and data modes for broader accessibility, relegating CW to specialized uses. By 2003, the International Telecommunication Union (ITU) revised its regulations at the World Radiocommunication Conference (WRC-03), eliminating the Morse code proficiency requirement for amateur radio licenses worldwide, which further diminished its mandatory role in spectrum allocations.^[40] Echoes of CW's efficiency persist in modern digital modes like FT8, a weak-signal protocol that achieves similar low-power, long-distance contacts by decoding signals down to -24 dB SNR, often outperforming traditional CW in noisy bands while requiring minimal operator intervention. In amateur radio, CW training remains integral to emergency communications preparedness, with organizations like the ARRL emphasizing Morse for fallback operations in scenarios where voice or data fail, such as during natural disasters.^[41]

Radio Applications

CW Telegraphy

CW telegraphy employs on-off keying (OOK) of a continuous carrier wave to transmit International Morse code, where the carrier is modulated by briefly turning it on for dots and longer for dashes, with defined intervals for spaces. In this system, a dot is represented by a short pulse of one time unit duration, while a dash is a longer pulse of three time units; the interval between elements (dots or dashes) within a character is one unit, between characters is three units, and between words is seven units.^[42] These timings, standardized for international radiotelegraphy, ensure consistent decoding across operators and equipment.^[43] Transmission involves manual keying of the carrier using a straight key or semi-automatic key (often called a "bug"), where the operator depresses the key to generate the on periods for dots and dashes according to the Morse code sequence. Straight keys require full manual control for each element, while semi-automatic keys mechanically produce consistent dash lengths and spaces through a vibrating arm, allowing the operator to focus on timing dots and character separations. At the receiver, decoding traditionally occurs aurally by trained operators who interpret the rhythmic tones at speeds of 20 to 40 words per minute (WPM), a proficiency developed through practice and enabling reliable copy under varying conditions. Early mechanical recorders, such as inkwriters or Mills (typewriter-based transcribers), automated initial decoding by printing dots and dashes on paper tape or typing characters, reducing operator fatigue for high-volume traffic.^[44]^[45]^[46]^[47] CW offers significant advantages in radio communications, particularly its ability to achieve high data rates within a narrow bandwidth, supporting up to 50 baud for rapid transmission while occupying as little as 50-100 Hz depending on keying speed. This efficiency stems from the binary-like on-off modulation, which concentrates power in the carrier and minimizes spectral spread, allowing selective filtering to enhance signal-to-noise ratio. In high-frequency (HF) bands, CW benefits from superior propagation characteristics, enabling long-distance contacts via ionospheric reflection where wider-band modes like voice may fail due to noise and fading; its narrow footprint permits operation in constrained spectrum allocations and excels in weak-signal scenarios, providing a 12-17 dB advantage over single-sideband voice.^[48]^[49]^[50]^[51] Essential equipment includes transmitters equipped with key jacks for connecting the manual or semi-automatic key, often integrated with a power amplifier to sustain the carrier during on periods. Receivers incorporate a beat frequency oscillator (BFO) to heterodyned the incoming RF signal with a local tone generator, producing an audible beat note typically around 800 Hz for comfortable aural decoding; this is crucial since unmodulated CW appears silent without the BFO.^[52]^[53]

Key Clicks and Artifacts

Key clicks in continuous wave (CW) radio transmissions refer to broadband transient emissions generated by abrupt on/off keying of the carrier signal, resulting in spectral splatter that extends well beyond the intended narrowband signal. These transients occur when the transmitter is switched without gradual rise and fall times, producing sharp edges in the envelope that excite wide-frequency components due to the Fourier transform properties of sudden changes. In severe cases, such as square-wave keying, the spectrum can spread up to 25 kHz at -60 dB relative to the carrier, causing interference to adjacent channels.^[54] The primary causes of key clicks include imperfect keying waveforms lacking sufficient rise/fall times—often less than 5 ms—and non-linearities in transmitter stages like Class-C amplifiers, which amplify the transients into harmonic-rich splatter. This interference manifests as audible "clicks" or "thumps" to receivers on nearby frequencies, degrading copyability of weak signals in crowded bands and potentially violating good operating practices. Effects are exacerbated at higher keying speeds, where faster transitions widen the spectrum further, sometimes reaching several kilohertz of out-of-band emission. To mitigate key clicks, operators employ keying filters or shaped waveforms, such as raised cosine or Gaussian envelopes with 5-10 ms rise/fall times, which confine the bandwidth to under 600 Hz at -60 dB while maintaining readability.^[55]^[54]^[56] Beyond key clicks, other common artifacts in CW transmissions include chirp, a perceptible frequency shift during the key-down period caused by oscillator drift from thermal or loading effects. For instance, in vintage crystal oscillators, keying can induce a downward frequency drift of hundreds of Hertz over the first second due to heating or power supply variations. Unintentional frequency modulation (FM) from mechanical vibrations or inadequate stabilization also generates unwanted sidebands, broadening the signal spectrum and mimicking low-level interference. These artifacts are typically measured using spectrum analyzers to visualize the envelope's frequency content and ensure compliance with emission standards.^[57] Regulatory bodies like the FCC impose limits on CW emission bandwidth under 47 CFR §97.307 to prevent harmful interference, defining occupied bandwidth as the band where mean power is attenuated at least 26 dB below the total power, with further suppression required for out-of-band emissions. For narrow CW, practical limits and recommendations often target around 250 Hz to fit within allocated sub-bands, though no explicit numerical cap exists for all frequencies; historical complaints about key clicks were prevalent in crowded amateur bands before the 1950s, when rudimentary equipment amplified such issues amid post-war band congestion.^[58]^[56]

Modern Radio Uses

In contemporary radio applications, continuous wave (CW) signals serve as foundational carriers in beacon systems designed for precise time dissemination and ionospheric monitoring. Time-signal stations like WWV, operated by the National Institute of Standards and Technology (NIST), transmit CW markers including second pulses and minute markers at 100% modulation depth to provide global synchronization references. These broadcasts occur across multiple high-frequency (HF) bands, specifically 2.5 MHz (at 2500 W), 5 MHz (10,000 W), 10 MHz (10,000 W), 15 MHz (10,000 W), and 20 MHz (2500 W), enabling receivers worldwide to calibrate clocks and frequency standards with high accuracy. Similarly, ionospheric sounders employ CW modes to assess propagation conditions by detecting noise levels and frequency shifts through single-frequency transmissions with extended integration times and narrow receiver bandwidths, operating in the 2.8–21.9 MHz range at intervals such as every 10 minutes. This CW-based approach facilitates automatic gain control and pre-scanning of HF channels, particularly in challenging high-latitude environments, yielding real-time data on ionospheric variability essential for reliable long-haul communications. Scientific monitoring leverages CW for specialized radio applications, including interferometry in radio astronomy and very low frequency (VLF) transmissions for submarine operations. In radio astronomy, CW signals form the basis for interferometric arrays that combine continuous receptions from multiple telescopes to achieve high-resolution imaging of celestial sources, as the unmodulated carrier nature allows precise phase correlation across baselines. Propagation beacons operating in CW mode further support scientific ionospheric studies by transmitting Morse-coded identifications, enabling researchers to map HF signal paths and atmospheric effects. For military and strategic purposes, VLF transmitters such as the AN/FRT-31 at NAA Cutler, Maine, utilize CW carriers at 24 kHz (with 2 MW output) to penetrate seawater up to 40 meters, providing submerged submarines with command and control messages via narrowband frequency-shift keying (FSK) overlaid on the carrier. These systems, including historical installations like those at 15.5 kHz (NSS Annapolis) and 21.4/23.4 kHz (NPM Lualualei), ensure resilient one-way broadcasts critical for naval operations. Digital hybrid modes integrate CW as a carrier for weak-signal propagation testing, enhancing amateur and experimental radio practices. The Weak Signal Propagation Reporter (WSPR) mode, part of the WSJT-X software suite, employs CW-derived carriers shifted by continuous single tones (1400–1600 Hz audio offsets) to probe MF and HF paths, detecting signals as weak as -28 dB signal-to-noise ratio (SNR) for global reporting networks. This enables automated mapping of propagation without manual intervention, often combined with CW beacons for dual-mode transmission across 10 kHz to 230 MHz. Software-defined radios (SDRs) further amplify CW's role in long-distance (DX) communications by generating precise CW signals for DXing, offering advantages like spectrum visualization to identify faint Morse transmissions amid noise, multi-band simultaneous monitoring, and digital filtering that boosts weak-signal recovery by up to 20–30 dB in dynamic range compared to analog rigs. CW's persistence in modern radio stems from its inherent advantages in energy efficiency and jamming resilience, particularly for low-power deployments. In Internet of Things (IoT) sensors, CW modulation—essentially on-off keying (OOK)—minimizes transmitter duty cycles and circuitry complexity, achieving power consumptions below 1 mW during bursts, which extends battery life in remote environmental monitors by factors of 5–10 over complex schemes like quadrature amplitude modulation (QAM). This efficiency suits ultra-low-power beacons in wireless sensor networks, where CW carriers enable sporadic data pings with minimal overhead. Additionally, CW's narrow bandwidth (typically <100 Hz) provides robustness against wideband jamming, as receivers can employ sharp filters to isolate the signal, maintaining communication links in contested spectra where broader modulations degrade by 10–15 dB under interference. These traits underpin CW's niche in jammed environments, such as tactical networks, where frequency agility and low detectability preserve operational integrity.

Radar Applications

Basic CW Radar

Basic CW radar systems transmit an unmodulated continuous wave signal and simultaneously receive echoes from targets, mixing the received signal with the transmitted signal in a receiver to generate a beat frequency that corresponds to the Doppler shift caused by moving objects. This homodyne receiver architecture simplifies the design by using the transmit signal directly as the local oscillator for downconversion, enabling direct extraction of the Doppler information without intermediate frequency stages.^[59]^[60] The Doppler shift f_d in a basic CW radar is determined by the formula

f_d = \frac{2 v f}{c}

where v is the radial velocity of the target relative to the radar, f is the transmitted frequency, and c is the speed of light. This shift produces an audio-frequency beat signal proportional to the target's velocity, allowing precise speed measurement but introducing range ambiguity since the continuous transmission provides no timing reference for distance calculation. Without modulation, absolute range cannot be resolved, limiting the system to velocity sensing and motion detection, as stationary targets produce no Doppler shift and cannot be distinguished from clutter. Detection reliability depends on achieving a sufficient signal-to-noise ratio (SNR) to ensure reliable target identification above the noise floor.^[60]^[61] These systems operate at low transmit powers, often in the milliwatt (mW) range, making them suitable for short-range applications where high power is unnecessary and compactness is prioritized. Early examples include experimental German CW radar developments in the 1930s, such as the system demonstrated in 1934 that detected a battleship in Kiel harbor, which laid groundwork for wartime applications. Modern uses encompass intrusion alarms that detect motion across perimeters via Doppler signatures, simple speed guns employed for traffic enforcement, where low-power operation suffices for ranges up to several hundred meters, and non-contact vital signs monitoring for detecting heart rate and respiration in medical and security applications.^[62]^[63]^[64]^[65]^[59]

Frequency-Modulated CW Radar

Frequency-modulated continuous wave (FMCW) radar employs a linear frequency sweep, known as a chirp, across a bandwidth B over a sweep duration T, enabling range measurement through the resulting beat frequency f_b in the mixed received and transmitted signals. The beat frequency is given by f_b = \frac{2 R B}{[c](/page/Speed_of_light) T}, where R is the target range and c is the speed of light.^[60] This modulation allows FMCW systems to resolve target distances without the need for pulsed transmissions, distinguishing it from unmodulated CW radar that primarily measures velocity via Doppler shift.^[60] Key advantages of FMCW radar include high range resolution defined by \Delta R = \frac{c}{2 B}, which achieves values as fine as 15 cm with a 1 GHz bandwidth, the ability to measure range and velocity simultaneously through phase analysis across multiple chirps, and elimination of precise pulse timing requirements, reducing complexity compared to pulsed radars.^[60]^[66] These features enable low-power operation with continuous transmission, improving sensitivity via extended integration time while maintaining multi-target discrimination.^[66] FMCW radar finds widespread use in automotive applications, such as 77 GHz systems for advanced driver-assistance systems (ADAS) introduced by manufacturers like Mercedes-Benz in the late 1990s and expanded in the 2000s for collision avoidance and adaptive cruise control. As of 2025, FMCW radar has become essential for higher levels of vehicle autonomy (Level 3 and above), with 4D imaging variants providing three-dimensional velocity mapping for enhanced perception in robotaxis and self-driving cars.^[67]^[68] It also serves in aircraft altimeters for precise height measurement above terrain, leveraging its resistance to environmental interference. In weather sensing, ultra-wideband FMCW variants provide high-resolution profiling of precipitation and snow depth from airborne platforms. Implementation typically involves sawtooth or triangular waveforms to generate the chirp, with the received signal processed via fast Fourier transform (FFT) to extract the beat frequency spectrum for range determination.^[66] Triangular modulation facilitates velocity estimation in a single sweep by comparing up- and down-chirps, while sawtooth requires multiple sweeps for Doppler resolution.^[69] Challenges from non-linear chirps, caused by voltage-controlled oscillator imperfections, are addressed through calibration algorithms that apply phase corrections or upsampling to restore linearity and maintain accuracy.^[70]

Optical Applications

CW Lasers

In optics, continuous wave (CW) lasers produce a steady beam of light with constant output power ranging from milliwatts to kilowatts, without the intermittent pulsing characteristic of other laser modes. This steady emission is achieved by continuously pumping the gain medium—typically via electrical discharge for gas lasers, optical excitation for solid-state lasers, or forward electrical bias for semiconductors—to sustain lasing action over extended periods. Unlike pulsed lasers, which deliver energy in short bursts, CW operation ensures a uniform irradiance suitable for applications requiring consistent illumination.^[71] Various types of CW lasers exist, categorized by their gain media. Gas lasers, such as the helium-neon (He-Ne) laser, operate at a wavelength of 632.8 nm in the visible red spectrum and are valued for their simplicity and reliability. Solid-state CW lasers, like the neodymium-doped yttrium aluminum garnet (Nd:YAG) at 1064 nm in the near-infrared, use crystalline hosts pumped by lamps or diodes for higher powers. Semiconductor diode lasers, compact and efficient, emit at diverse wavelengths from ultraviolet to infrared, depending on the material composition, and dominate in consumer and industrial uses due to their low cost and direct electrical pumping. These systems generally maintain output stability with power fluctuations below 1%, often achieved through active feedback mechanisms.^[71]^[72] The core principle of CW laser operation involves maintaining a steady population inversion in the gain medium, where more atoms or molecules occupy the upper energy level than the lower one, enabling net stimulated emission. This inversion is balanced by continuous pumping to counteract spontaneous emission and losses, with lasing occurring above a threshold where gain equals cavity losses. The threshold pump power P_{th} can be expressed as

P_{th} = \frac{h\nu \Delta N}{\sigma \tau},

where h\nu is the photon energy, \Delta N represents the required population inversion density, \sigma is the stimulated emission cross-section, and \tau is the lifetime of the upper laser level; this formula derives from rate equations governing photon and population dynamics in steady state. In practice, the gain medium is placed within a resonant cavity to amplify the light recursively until equilibrium is reached.^[73] A key advantage of CW lasers is their high temporal and spatial coherence, with stabilized He-Ne models achieving coherence lengths on the order of kilometers, far exceeding typical incoherent sources. This property supports precise applications such as optical alignment in surveying and manufacturing, where a stable beam ensures accurate targeting over long distances, and holography, where extended coherence enables interference patterns for three-dimensional imaging. These attributes make CW lasers indispensable in fields demanding uninterrupted, high-fidelity light output.^[74]

Laser Physics and Uses

In continuous-wave (CW) laser operation, the steady-state behavior is governed by rate equations describing the dynamics of the photon number n inside the cavity and the population inversion N between the lasing levels. The rate equation for the photon number is given by

\frac{dn}{dt} = \frac{\Gamma \sigma N n}{h \nu} - \frac{n}{\tau_c} + R_{sp},

where \Gamma is the confinement factor, \sigma is the stimulated emission cross-section, h\nu is the photon energy, \tau_c is the cavity photon lifetime, and R_{sp} accounts for spontaneous emission noise; for the inversion,

\frac{dN}{dt} = R - \gamma N - \frac{\Gamma \sigma N n}{h \nu},

with R as the pump rate and \gamma the inversion decay rate. In steady-state CW conditions, derivatives are zero, yielding n = n_0 (N - N_{th}) where N_{th} is the threshold inversion, enabling constant output power without oscillations. The fundamental linewidth of a CW laser, limited by quantum phase noise, is described by the Schawlow-Townes formula:

\Delta \nu = \frac{h \nu (\Delta \nu_c)^2}{4 \pi P_{out}},

where \Delta \nu_c is the cold-cavity linewidth and P_{out} is the output power; this predicts linewidths below 1 Hz for high-power systems with long cavities.^[75] To achieve single-mode operation and mode stability in CW lasers, intracavity etalons filter unwanted longitudinal modes, selecting a single frequency with linewidths narrowed to mHz levels. Frequency locking to external references, such as in the iodine-stabilized He-Ne laser at 633 nm, uses saturated absorption spectroscopy in ^{127}I_2 vapor to stabilize the output to hyperfine transitions, achieving fractional frequency stability of $10^{-12} over seconds. CW lasers find essential applications in medicine, where the CO_2 laser at 10.6 \mum delivers continuous thermal energy for precise soft-tissue surgery, enabling vaporization and hemostasis with minimal collateral damage in procedures like lesion removal. In optical communications, distributed feedback (DFB) diode lasers at 1550 nm provide stable CW output for long-haul fiber-optic transmission, leveraging low attenuation in silica fibers for data rates exceeding 100 Gbps over thousands of kilometers. For high-resolution spectroscopy, tunable CW dye lasers, pumped by argon-ion sources, offer continuous wavelength coverage from 400 to 800 nm with sub-MHz linewidths, facilitating Doppler-free studies of atomic and molecular spectra.^[76]^[77]^[78] Post-2000 advancements have produced ultrastable CW lasers critical for optical clocks, where external-cavity diode lasers locked to Fabry-Pérot cavities achieve Allan deviations below $10^{-15} at 1 s, enabling ytterbium and strontium lattice clocks with uncertainties rivaling cesium standards. Power scaling in fiber lasers has reached 100 kW CW output by the 2020s, using ytterbium-doped architectures with coherent beam combination to maintain near-diffraction-limited quality for industrial welding and cutting of thick metals.^[79]^[80]

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May 30, 2021 · Some common values for frequency stability are ±20 ppm, ±50 ppm and ±100 ppm over a specified temperature range. Again, it is possible to order ...
[17]
Fessenden and the Early History of Radio Science
Sep 3, 1994 · Marconi, following the lead of Hertz, employed such a spark transmitter, but his antenna was a monopole type, a wire fed against ground.
[18]
First Wireless Radio Broadcast by Reginald A. Fessenden, 1906
Jun 14, 2022 · December 21, 1906: Alternator-transmitter used for wireless telephony. Fessenden gives a major demonstration of his new high frequency ...Missing: quasi- | Show results with:quasi-
[19]
Ernst F. W. Alexanderson - Engineering and Technology History Wiki
Mar 5, 2025 · Beginning in 1904, Alexanderson designed a series of high-frequency alternators for use in radio as sources of transmitter power which provided ...
[20]
[No. 79] The Alexanderson Alternator — An Axial-flux Marvel - JMAG
Mar 3, 2025 · Power output, 10−200 kW. Frequency, 10−100 kHz. Configuration, Axial ... A few Alexanderson alternators were in regular use up to and beyond the ...
[21]
Spark-gap transmitter - Open Tesla Research - Jimdo
These transmitters radiated an extremely "dirty" wide band signal which could greatly interfere with the reception of other transmissions on nearby frequencies.
[22]
https://www.jmag-international.com/engineers_diary/079/
[23]
[PDF] History of Naval Ships Wireless Systems
By 1924, frequency and power limitations were applied to spark gap transmitters and they were totally banned in the United States by 1927. Many amateur radio ...Missing: broad spectrum
[24]
Radio Research Paper - History of Naval Comm
By 1924, frequency and power limitations were applied to spark gap transmitters and they were totally banned in the United States by 1927.
[25]
Have you ever heard of the Alexanderson alternator? | Megger
Mar 17, 2020 · An Alexanderson alternator was installed in the Fessenden station at Brant Rock in Massachusetts and, on 24th December 1906, this 2 kW, 100 kHz ...
[26]
Audion – 1906 - Magnet Academy - National MagLab
The name De Forest chose for the invention hints at the fact that the Audion detected radio signals, served as a rectifier (a device that converts alternating ...Missing: continuous wave<|control11|><|separator|>
[27]
Edwin H. Armstrong House - National Historic Landmarks (U.S. ...
Armstrong's regenerative circuit was the first radio amplifier and it became the basis of the continuous-wave transmitter that remains key to radio broadcasting ...
[28]
[PDF] The Continuous Wave: Technology and American Radio, 1900-1932
... Fessenden's rotary spark transmitter. 89. 3. Elwell's 100 watt Poulsen arc. 109 ... 1901 Fessenden discovers heterodyne principle. Marconi reports ...<|control11|><|separator|>
[29]
NIST and the Titanic: How the Sinking of the Ship Improved Wireless ...
Apr 13, 2022 · The tragedy of the Titanic raised awareness that improvements to wireless communication were needed and led to new regulations and legislation by Congress.
[30]
[PDF] Below 535 A Historical Review of Continuous Wave Radio ...
For a spark transmitter, the effective bandwidth is literally hundreds of kilohertz! See reference 5 for a more thorough discussion of occupied bandwidth. 3.
[31]
Armstrong's Super-Regenerative Circuit (1922) - Early Radio History
Super-regeneration is a clever combination of electrical phenomena, based on the regenerative receiver, using a second tube to control the grid of the receiver ...
[32]
CW Radiotelegraphy - A Robust mode - Amazing Amateur Radio
Jan 29, 2020 · Low transmitter power requirements to establish communication over long distances under difficult conditions. Very weak CW signals are ...
[33]
History of Morse Code - International CW Council
Oct 14, 2021 · Morse Code was vital for ship to shore & military use until replaced by Satellite communications in the 1990s. This is a wonderful photo taken ...Missing: aviation | Show results with:aviation<|control11|><|separator|>
[34]
https://vu2nsb.com/cw-digital-radio/cw-radiotelegraphy/
[35]
ARRL International DX CW Contest
Aug 16, 2023 · To encourage W/VE stations to expand knowledge of DX propagation on the HF and MF bands, improve operating skills, and improve station ...Missing: amateur | Show results with:amateur
[36]
[PDF] GMDSS and SAR 1999 - International Maritime Organization
It became fully operational on 1 February 1999. On that date, the. Morse Code was phased out and all passenger ships and all cargo ships of 300 gross tonnage ...
[37]
International Beacon Project Transmission Schedule - NCDXF
Each beacon transmits once on each band once every three minutes, 24 hours a day. A transmission consists of the callsign of the beacon sent at 22 words per ...Introduction · Locations and Grid Squares · Windows 3.1 · Early History
[38]
The Code lives on: how Morse is still not dead
Oct 20, 2015 · In 2003, the international requirement for proficiency in Morse code was dropped, and many hams (like myself) are no longer able to use it.
[39]
Weak-Signal Performance of Common Modulation Formats
Mar 23, 2025 · SSB is the least sensitive, followed by RTTY and PSK31. CW performs better than RTTY and PSK31. WSPR has the best SNR performance.Missing: mimicking | Show results with:mimicking
[40]
None
### Summary of Morse Code Timings from Rec. ITU-R M.1677
[41]
Timing and spectrum of morse code
The fact that the 5 Hz peaks coincide with the dots is a direct consequence of the morse timing rules. ... For international telegraphy, the current alphabet and ...
[42]
A Totally Retro Mode Makes a Comeback - | Nuts & Volts Magazine
Mar 7, 2017 · For CW reception, the receiver requires a beat frequency oscillator ... When greater speed is needed, a “bug” (semi-automatic key) is used.
[43]
U.S. Navy Morse Code Training - WB3GCK QRP Amateur Radio
Nov 10, 2018 · The operator keying to you for practice should transmit each individual character at the standard rate of 20 words per minute. He should ...
[44]
Navy Automated Morse Code (CW) Equipment
Navy automated Morse code equipment included paper tape systems, code recorders, keyers, perforators, and tape pullers, using paper tape for transmission.
[45]
Morse code ink writer, 1876 - Powerhouse Collection
This is a Morse code ink writer patented in 1876 and made by the Western Electric Company of Chicago and New York. The New South Wales Government Railways ...
[46]
An Intuitive Explanation of CW Bandwidth - W8JI
12 WPM is about 10 baud. One of the slowest RTTY baud rates (45.45 bauds) is close to our 60 WPM test keying rate. (In computer signaling, the term bps has ...
[47]
Bandwidth of various modulation modes: CW, SSB, FM, fast-scan TV
CW uses the least bandwidth of all commonly used modes; all you really need to get across clearly is a single tone so that the receiving station can hear when ...<|separator|>
[48]
High Frequency Communications Features Highs and Lows
Feb 1, 2020 · High frequency radio provides a means to continue communicating even beyond the line of sight by leveraging the ionosphere to refract radio signals back to ...
[49]
Technician Licensees -- Why Not Try Low Power HF CW? - eHam.net
Aug 12, 2014 · Simply put, CW is a highly effective, engaging and elegantly simple mode. Relative to phone (SSB), CW can provide a 12-17 dB advantage - that's ...
[50]
What is the Morse Code: What is CW - Electronics Notes
To generate the characteristic Morse tone, the radio receiver must be equipped with a beat frequency oscillator, BFO, or carrier insertion oscillator, CIO. This ...
[51]
[PDF] CW, the coolest mode. AK0Z – Larry
A BFO or beat frequency oscillator generates a sidetone which is beat to ... Straight key, semi automatic or(bug), single paddle or(cootie, side swiper) ...Missing: equipment | Show results with:equipment
[52]
[PDF] Key-clicks and CW Waveform shaping
CW transmitted with poor waveform shaping causes interference that is heard as clicks and thumps by other CW operators on nearby frequencies.
[53]
What creates CW key clicks? - W8JI
Clicks are most problematic when we try to copy weak signals next to moderately strong signals. If you only operate on empty bands, run low power, and never ...
[54]
Why Key Clicks?, October 1966 QST - RF Cafe
Jul 6, 2021 · RC networks are used in the transmitter circuits to tame the edges so that they do not turn on and off so quickly and in doing so reduce the ...
[55]
Causes of CW keyclicks - W8JI
Technical resource and information on receiving and transmitting keyclicks and how to modify radios to reduce clicks.
[56]
97.307 Emission standards. - Title 47 - eCFR
The authorized bandwidth is 2.8 kHz except in the 2200 m band and 630 m band. In the 2200 m band and the 630 m band the symbol rate must not exceed 300 bauds, ...
[57]
Benefits of Coherent Low-IF for Vital Signs Monitoring Using ...
Aug 5, 2025 · Although the homodyne CW radar has the simplest architecture, its performance would be limited by the flicker noise from the mixer and the ...
[58]
[PDF] Principles of Classical and Modern Radar Continuous Wave (CW ...
FMCW Radar is a low cost radar system, often used in shorter range applications. The system is simple to fabricate but requires care to obtain high accuracy.
[59]
[PDF] Continuous Wave Radar
A CW-radar transmitting a unmodulated power can measure the speed only by using the Doppler- effect. It cannot measure a range and it cannot differ between two ...
[60]
[7.0] The Battle Of The Beams - Vectors
Aug 1, 2024 · The German researchers put together a continuous wave radar system, and in March 1934 they used it to detect a battleship in Kiel harbor. By ...
[61]
[PDF] Speed-Measuring Devices Specifications: Down-the-Road Radar ...
Apr 1, 2016 · Set the generator to a frequency of 160 MHz with an output of 10 mW, as measured by the power meter, with no more than 1 mW reflected power.
[62]
Traffic Surveillance using Low Cost Continuous Wave (CW) Doppler ...
Low cost un-modulated continuous wave (CW) radar (CW Doppler radar) can be used to measure the speed of a vehicle. Traditionally, a radar gun, a lidar gun ...
[63]
New microwave sensors for intrusion detection systems - IEEE Xplore
Intrusion detection systems based on the utilisation of continuous wave (CW) radar and Doppler effect have several advantages over electrooptic sensors, ...Missing: alarms | Show results with:alarms
[64]
[PDF] 24GHz FMCW Radar, Basic Theory and Real-World Measurements
Radar sensitivity is based on received energy, which is the product of power and time. Pulsed radars achieve good range resolution by using short pulses and as ...Missing: formula | Show results with:formula<|control11|><|separator|>
[65]
[PDF] Collision Avoidance W-Band FMCW Radars in an Altimeter ...
The frequency modulated continuous wave (FMCW) radar principle has been used in aircraft radio altimeters to measure height above the surface of the Earth.
[66]
[PDF] Triangular and Ramp Waveforms in Target Detection with a ... - CORE
This thesis studies how triangular chirps are used in target detection and parameter estimation with FMCW radar, comparing them to ramp chirps.
[67]
A Novel Nonlinearity Correction Algorithm for FMCW Radar Systems ...
The algorithm uses a new upsampling theory with fixed structure interpolators to correct VCO nonlinearity in FMCW radars, improving range accuracy and ...
[68]
[PDF] An Overview Of Lasers and Their Applications A Senior Project By ...
May 26, 2020 · There are two forms of laser power output known as continuous wave or pulsed operation lasers. In continuous wave (cw) lasers the laser ...
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HeNe Lasers: Red - Thorlabs
Hello Li, thanks for reaching out to us. The typical coherence length of our HeNe lasers is >30cm. Linearly polarized versions tend to have greater coherence ...<|control11|><|separator|>
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[PDF] Chapter 7 Lasers
We want to derive the equations of motion for th population inversion, or population in the upper laser level and the photon number in that mode, see Figure ...Missing: formula | Show results with:formula
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[PDF] Stabilized Helium Neon Laser Systems
single-longitudinal-mode systems have a coherence length mea- sured in kilometers, and they exhibit excellent power stability for long periods of time. They ...
[72]
[PDF] schawlow-townes-1958.pdf
To select just one from among the very many modes possible within the line width, the stimulated emission of radiation with one chosen direction of propagation.
[73]
Different CO2 laser vaporization protocols for the therapy of oral ...
Use of the CO(2) laser (λ = 10.6 μm, continuous wave, defocused) is an established procedure for the treatment of premalignant lesions.
[74]
[PDF] High-Power CW-DFB LDs for Optical Communications
In this paper, we report our activities to achieve a low driving current for WDM applications. As high power tech- nologies expand, we are also developing ...
[75]
[PDF] CW DYE LASERS - Time and Frequency Division
The cw dye laser is a well-established tool of optical science. It plays the premier role as a source of tunable radiation in the visible and near-visible.<|control11|><|separator|>
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Optical atomic clocks | Rev. Mod. Phys.
Jun 26, 2015 · In this article a detailed review on the development of optical atomic clocks that are based on trapped single ions and many neutral atoms is provided.
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100 kW CW Fiber Laser for Industrial Applications - ResearchGate
Oct 4, 2025 · Ytterbium fiber laser combines record 101.3 kW output power, CW operational mode and an excellent beam quality. Beam parameter product (BPP) ...Missing: 2020s | Show results with:2020s