Published: 2026-05-24 Modern phased array radar and communications systems depend on precise frequency and time references for beam steering, coherent signal processing, and synchronization across distributed aperture elements. In conventional architectures, a GNSS-disciplined oscillator (GPSDO) serves as the primary reference, periodically calibrating the local oscillator to UTC-traceable accuracy. However, an increasing number of operational scenarios—ranging from contested electromagnetic environments to indoor and underground deployments—deny access to GNSS signals, requiring the system to operate autonomously on its local reference clock. This application note examines the technical requirements for operating phased array systems in GPS-denied conditions, analyzes the relative merits of rubidium atomic frequency standards (RAFS) versus oven-controlled crystal oscillators (OCXO) for holdover applications, and presents the BRIDZA series rubidium clocks as an optimal solution for maintaining the frequency stability, phase coherence, and timing accuracy demanded by high-performance phased array architectures during extended GPS-denied holdover periods. Holdover is defined as the period during which a clock operates autonomously, without external calibration or disciplining from a reference source such as GNSS. The key performance metric for holdover is time error (TE) accumulated from the moment of reference loss, expressed as: $$TE(t) = \int_0^t \Delta f(\tau) \, d\tau + TE_0$$ where $\Delta f(\tau)$ is the fractional frequency offset at time $\tau$ and $TE_0$ is the time error at the onset of holdover. The critical clock parameter governing holdover is the frequency stability of the free-running oscillator, which determines how quickly the time error grows after the reference is lost. For an oscillator with a constant fractional frequency offset $\Delta f / f_0$, the time error grows linearly: $$TE(t) = \frac{\Delta f}{f_0} \cdot t$$ For example, a frequency offset of $1 \times 10^{-10}$ produces a time error of approximately 8.64 ns per day (10 ns/day for practical calculations). The required holdover performance depends on the specific phased array application, its operating mode, and the acceptable performance degradation. Table 1 summarizes typical requirements across several application domains. Table 1: Typical Phased Array Holdover Requirements | Application | Frequency Stability Required | Time Error Budget (24 hr) | Typical Holdover Duration | |---|---|---|---| | Ground-based surveillance radar | ≤ 1 × 10⁻¹⁰ | < 10 µs | 24–72 hours | | Shipboard phased array (AEGIS-type) | ≤ 5 × 10⁻¹¹ | < 5 µs | 24–48 hours | | Airborne AESA radar | ≤ 1 × 10⁻¹⁰ | < 10 µs | 4–24 hours | | Distributed MIMO/Netted radar | ≤ 1 × 10⁻¹¹ | < 1 µs | 12–24 hours | | Electronic warfare (ESM/ELINT) | ≤ 5 × 10⁻¹⁰ | < 50 µs | 8–24 hours | | SATCOM phased array terminal | ≤ 1 × 10⁻¹⁰ | < 10 µs | 24–72 hours | | 5G beamforming base station | ≤ 1.6 × 10⁻⁸ | < 1.5 ms | 24–72 hours | For most radar and communications phased array applications, the frequency stability requirement during holdover falls in the range of $1 \times 10^{-10}$ to $1 \times 10^{-11}$ (measured over averaging times of 1–100 seconds), with accumulated time error budgets of 1–10 µs over 24 hours. The Allan deviation (ADEV), $\sigma_y(\tau)$, is the standard metric for characterizing oscillator frequency stability. For holdover applications, the relevant measurement is typically at averaging times of 1 second to 10,000 seconds, as this range governs the short-to-medium-term frequency wandering that accumulates during autonomous operation. The phase error $\Delta\phi$ at a given microwave frequency $f_{RF}$ due to frequency offset $\Delta f / f_0$ of the reference is: $$\Delta\phi = 2\pi \cdot f_{RF} \cdot \frac{\Delta f}{f_0} \cdot \Delta t$$ For an X-band radar at 10 GHz with a reference frequency offset of $1 \times 10^{-10}$ and a coherent processing interval of 10 ms, the accumulated phase error is: $$\Delta\phi = 2\pi \times 10^{10} \times 10^{-10} \times 0.01 = 0.063 \text{ radians} \approx 3.6°$$ This level of phase error is generally acceptable for most radar processing modes. However, if the frequency offset grows to $1 \times 10^{-9}$, the phase error becomes 36°, which would significantly degrade coherent integration gain and clutter rejection performance. This illustrates the critical importance of maintaining frequency stability below $1 \times 10^{-9}$ during holdover for even short processing intervals. While rubidium clocks derive their frequency from an atomic transition, the physical package and electronics introduce residual aging effects that cause the output frequency to drift slowly over time. The primary aging mechanisms include: Light shift (AC Stark shift): The rubidium spectral lamp illuminates the resonance cell with optical radiation at 780 nm and 794 nm (the D-lines of rubidium). Imperfect filtering and cell buffer gas pressure cause a small frequency shift proportional to the lamp intensity. As the lamp ages (rubidium migration, electrode sputtering), the light shift changes, producing frequency drift. Buffer gas effects: The resonance cell contains a buffer gas (typically a mixture of nitrogen and argon or neon) to reduce wall collisions and broaden the magnetic field-insensitive clock transition. Slow chemical reactions between the buffer gas and cell walls, as well as permeation through the cell envelope, gradually alter the buffer gas composition and pressure, changing the buffer gas shift. C-field drift: The quantization magnetic field (C-field) applied to the resonance cell determines the specific Zeeman sublevel selected for the clock transition. Drifts in the C-field current or magnetic shielding effectiveness change the field-dependent frequency shift. Crystal oscillator aging: The local crystal oscillator (VCXO) that is locked to the atomic resonance also contributes residual aging, particularly at short averaging times where the servo loop gain is insufficient to fully suppress crystal wander. Well-characterized rubidium clocks exhibit aging rates that improve with operational time: - First month of operation: $1 \times 10^{-10}$ to $5 \times 10^{-10}$ per month - After stabilization (1–6 months): $< 5 \times 10^{-11}$ per month - Mature operation (after 1 year): $< 1 \times 10^{-11}$ per month (in premium units) These rates are one to two orders of magnitude better than comparable OCXO aging, and critically, they tend to be monotonic and predictable, enabling effective correction. Several techniques can further reduce the effective aging of a rubidium clock during holdover: Pre-holdover frequency calibration: Before entering holdover, the system determines the current frequency offset by comparison with the GNSS reference. If the aging rate has been characterized through historical data, the system can model the expected frequency trajectory during holdover and pre-compensate accordingly. Real-time aging models: The most common approach fits the measured frequency offset to a polynomial model during GPS-locked operation: $$\hat{y}(t) = y_0 + \dot{y} \cdot (t - t_0) + \frac{1}{2}\ddot{y} \cdot (t - t_0)^2$$ where $y_0$ is the frequency offset at the start of holdover ($t_0$), $\dot{y}$ is the linear aging rate, and $\ddot{y}$ is the quadratic aging rate. The frequency correction is then applied during holdover based on this model, reducing the residual aging error. Modern implementations use Kalman filtering or recursive least-squares algorithms to continuously update the model parameters while locked to GNSS. Frequency memory with look-up tables: For systems with known deployment conditions and historical operational data, look-up tables indexed by temperature, operational age, and g-sensitivity can provide pre-computed correction values that are applied during holdover. Adaptive correction using redundant oscillators: In systems employing multiple rubidium clocks (common in high-reliability phased array architectures), the relative frequency between clocks can be monitored and used to estimate and correct drift, even during GNSS denial, assuming the clocks have characterized differential aging. With a well-characterized aging model and frequency pre-calibration, the residual frequency error during holdover can be reduced by a factor of 5–10× compared to the raw aging rate. For a rubidium clock with a stabilized aging rate of $2 \times 10^{-11}$/month, a linear correction model can reduce the effective holdover drift to approximately $2 \times 10^{-12}$/day or better, corresponding to a time error accumulation of less than 200 ns per day. The BRIDZA series rubidium atomic frequency standards are engineered specifically for applications requiring extended GPS-denied holdover capability in demanding operational environments. The product line includes several models optimized for different size, weight, power, and cost (SWaP-C) profiles while maintaining the fundamental advantages of the rubidium atomic reference. Table 3: BRIDZA Rubidium Clock Holdover Performance Summary | Parameter | BRIDZA-R100 | BRIDZA-R200 | BRIDZA-R300 | |---|---|---|---| | Output Frequency | 10 MHz | 10 MHz | 10 MHz | | Frequency Accuracy (at delivery) | ≤ ±5 × 10⁻¹¹ | ≤ ±5 × 10⁻¹¹ | ≤ ±2 × 10⁻¹¹ | | Short-term stability (ADEV, τ = 1 s) | ≤ 3 × 10⁻¹¹ | ≤ 2 × 10⁻¹¹ | ≤ 1 × 10⁻¹¹ | | Short-term stability (ADEV, τ = 10 s) | ≤ 8 × 10⁻¹² | ≤ 5 × 10⁻¹² | ≤ 3 × 10⁻¹² | | Short-term stability (ADEV, τ = 100 s) | ≤ 3 × 10⁻¹² | ≤ 2 × 10⁻¹² | ≤ 1 × 10⁻¹² | | Aging rate (after stabilization) | ≤ 3 × 10⁻¹¹/month | ≤ 2 × 10⁻¹¹/month | ≤ 5 × 10⁻¹²/month | | Temperature coefficient | ≤ 3 × 10⁻¹¹/°C | ≤ 2 × 10⁻¹¹/°C | ≤ 1 × 10⁻¹¹/°C | | G-sensitivity | ≤ 5 × 10⁻⁹/g | ≤ 3 × 10⁻⁹/g | ≤ 1 × 10⁻⁹/g | | Holdover performance (24 hr, TE) | < 1 µs | < 500 ns | < 200 ns | | Holdover performance (72 hr, TE) | < 3 µs | < 1.5 µs | < 1 µs | | Warm-up time (to lock) | < 5 min | < 4 min | < 3 min | | Warm-up time (to spec accuracy) | < 8 min | < 6 min | < 5 min | | Operating temperature range | −40°C to +70°C | −40°C to +70°C | −40°C to +70°C | | Power consumption | 8 W typical | 10 W typical | 15 W typical | | Size (L × W × H) | 100 × 100 × 38 mm | 120 × 120 × 45 mm | 150 × 150 × 50 mm | | Weight | 0.35 kg | 0.55 kg | 0.85 kg | | Phase noise (10 MHz, at 1 Hz offset) | −110 dBc/Hz | −115 dBc/Hz | −120 dBc/Hz | | Phase noise (10 MHz, at 10 Hz offset) | −130 dBc/Hz | −135 dBc/Hz | −140 dBc/Hz | | Phase noise (10 MHz, at 100 Hz offset) | −145 dBc/Hz | −148 dBc/Hz | −150 dBc/Hz | The BRIDZA-R200, as a representative mid-range model, achieves a 24-hour holdover time error of less than 500 ns. This performance derives from the combination of: - Intrinsic aging: The stabilized aging rate of ≤ 2 × 10⁻¹¹/month corresponds to a daily frequency offset of ≤ 6.7 × 10⁻¹³, producing a time drift of ≤ 58 ns/day. - Temperature sensitivity: With DTCXO reducing the effective coefficient to ≤ 2 × 10⁻¹¹/°C, a ±10°C temperature excursion produces ≤ 2 × 10⁻¹⁰ frequency offset, contributing ≤ 17 µs/day in the worst case but ≤ 50 ns in typical indoor environments. - Residual calibration uncertainty: The frequency offset at the onset of holdover, after GNSS calibration, is typically ≤ 1 × 10⁻¹², contributing ≤ 86 ns over 24 hours. The RSS (root sum square) combination of these contributions for a typical operational scenario yields a 24-hour holdover time error of approximately 100–500 ns, depending on the thermal environment and calibration quality. This performance is consistent with the needs of all phased array applications listed in Table 1. Figure 1 (conceptual) illustrates the typical Allan deviation behavior of the BRIDZA-R200 during GPS-locked and holdover operation: GPS-locked mode: The output frequency is disciplined to GPS, achieving stabilities of $1 \times 10^{-12}$ at τ = 1 s (limited by GPS signal noise) and $1 \times 10^{-13}$ to $1 \times 10^{-14}$ at τ = 10,000 s (limited by the GPS system time standard). Holdover mode: The output reverts to the intrinsic rubidium clock stability, with $2 \times 10^{-11}$ at τ = 1 s and improving to $2 \times 10^{-12}$ at τ = 100 s. At longer averaging times (τ > 1,000 s), the stability is governed by the aging rate, approximately $2 \times 10^{-11}$/month, which corresponds to $\sigma_y \approx 8 \times 10^{-15}$ at τ = 1 month. The critical observation is that the rubidium clock maintains its stability well beyond the crossover point with OCXO performance, ensuring that holdover performance remains excellent for durations spanning hours to weeks. Phase noise of the reference oscillator directly impacts the performance of phased array systems, particularly for: - Clutter cancellation: Close-in phase noise (1–100 Hz offset) limits the achievable clutter suppression in ground-based radars. - Doppler resolution: Phase noise in the 100 Hz–10 kHz offset range affects the minimum detectable velocity in pulse-Doppler processing. - Spurious-free dynamic range: Wideband phase noise (10 kHz–1 MHz offset) limits the receiver dynamic range. The BRIDZA series achieves phase noise performance of ≤ −115 dBc/Hz at 1 Hz offset and ≤ −148 dBc/Hz at 100 Hz offset (BRIDZA-R200), which is sufficient for all but the most demanding low-clutter radar applications. For applications requiring even lower close-in phase noise, the BRIDZA-R300 provides ≤ −120 dBc/Hz at 1 Hz offset, achieved through an enhanced VCXO design with higher resonator Q-factor. The increasing prevalence and sophistication of GNSS disruption threats—jamming, spoofing, environmental interference, and operational denial—make GPS-independent holdover capability an essential design requirement for modern phased array radar and communications systems. The choice of local oscillator technology is the single most important factor determining holdover performance. Rubidium atomic frequency standards offer a compelling combination of atomic-referenced long-term stability, manageable SWaP-C characteristics, and mature, proven technology. Their fundamental advantage over OCXOs for holdover applications—stability improvement rather than degradation over longer averaging times—translates to holdover performance that is 100–1000× superior to crystal-based alternatives over periods of 24 hours or more. The BRIDZA series rubidium clocks, with 24-hour holdover time errors of less than 500 ns (BRIDZA-R200) and less than 200 ns (BRIDZA-R300), provide the frequency stability, phase noise performance, and environmental robustness required by high-performance phased array systems operating in GPS-denied environments. Combined with proper aging correction models, temperature management, and system integration practices, BRIDZA rubidium clocks enable phased array systems to maintain full operational capability during extended periods of GNSS denial—a capability that is no longer a luxury but an operational necessity. BRIDZA Precision Timing Division — Delivering Precision Timing for GPS-Denied Operations For technical inquiries and product specifications, contact the BRIDZA applications engineering team.