Attofarad
Understanding the Attofarad
At millimeter-wave frequencies, the parasitic capacitances that RF engineers must contend with shrink to unimaginably small values — tens of attofarads, or tens of millionths of a picofarad. At low frequencies, these capacitances are irrelevant. At 77 GHz, they dominate circuit behavior.
Why Attofarads Matter at mmWave
Reactance is inversely proportional to frequency and capacitance: X_C = 1/(2πfC). At 1 GHz, a 50 aF capacitor has a reactance of 3.2 megohms — essentially an open circuit. At 77 GHz, the same 50 aF capacitor has a reactance of 41 ohms — comparable to the characteristic impedance of the transmission line and significant enough to shift the resonant frequency of a matching network by hundreds of MHz.
Parasitic Extraction at mmWave
Accurate simulation of mmWave circuits requires electromagnetic extraction of all parasitic capacitances from the physical layout — including capacitances between bond pads, between via stubs and ground planes, and between adjacent transmission lines. 3D EM solvers (HFSS, CST) compute these parasitic elements from the actual physical geometry, providing the attofarad-accurate models needed for successful first-pass mmWave circuit design.
Key Equations
An Attofarad (aF) is a unit of electrical capacitance equal to 10⁻¹⁸ farads — one quintillionth of a farad. In the context of RF and...
Key specifications:
77 GHz | 50 a | 140 GHz | 15 a | 80 a | 200 ohm
Power: P(dBm) = 10log(PmW), 0dBm = 1mW
Comparison
| Aspect | Attofarad Spec | Typical Range | Impact | Design Note |
|---|---|---|---|---|
| Primary function | An Attofarad (aF) is a unit of electrica... | Application-dep. | Critical | Verify in sim |
| Operating range | A 50 aF parasitic capacitance has a reac... | Application-dep. | Critical | Verify in sim |
| Performance | At low frequencies, these capacitances a... | Application-dep. | Critical | Verify in sim |
| Integration | At 77 GHz, they dominate circuit behavio... | Application-dep. | Critical | Verify in sim |
| Trade-off | Why Attofarads Matter at mmWave Reactanc... | Application-dep. | Critical | Verify in sim |
Frequently Asked Questions
How is an attofarad measured?
Direct measurement of individual attofarad-level capacitances is extremely challenging. In practice, they are characterized indirectly through S-parameter measurements of the complete circuit or structure, followed by model extraction using optimization-based fitting. The parasitic capacitance values are inferred from the measured S-parameter response rather than measured in isolation. Specialized capacitance measurement instruments (like the Keysight E4990A) can measure down to approximately 1 femtofarad (1000 aF) at low frequencies, but attofarad-level values at mmWave frequencies require S-parameter-based extraction.
Can EDA tools accurately model attofarad parasitics?
Schematic-level circuit simulators cannot — they only include the parasitic models explicitly provided in the component models. Layout-level EM extraction tools (integrated into EDA platforms like Cadence Virtuoso or Keysight ADS) can extract parasitic capacitances to attofarad accuracy by solving Maxwell's equations over the physical layout geometry. This EM-circuit co-simulation is mandatory for mmWave circuit design above 30 GHz.
What is the typical Cgd of a mmWave GaN HEMT?
For a 4×50 μm GaN HEMT at 77 GHz, Cgd is typically 15–50 aF depending on bias point and technology node. This feedback capacitance directly determines the transistor's maximum available gain (MSG/MAG) and stability factor. At lower frequencies, Cgd is negligible compared to Cgs (gate-source capacitance, typically 200–500 fF). At mmWave, the ratio Cgd/Cgs approaches values that make the transistor conditionally stable, requiring careful neutralization circuit design to prevent oscillation.