The power distribution network (PDN) within a PCB is constructed with conductors, yet its characteristics encompass an impedance spectrum. Interestingly, despite the perception of direct current (DC) power delivery, actual PCB power conditioning involves a departure from pure DC behavior. In practicality, true DC systems are uncommon; instead, real-world setups involve digital components that draw current intermittently rather than in a continuous manner as typical of DC circuits.
This conveys a paradox: while a DC-driven system might intuitively warrant DC analysis, the inherent behavior of digital components—drawing current intermittently in the time/frequency domain—necessitates scrutiny of PDN impedance. Particularly in the realm of high-speed digital design, assessing PDN impedance holds significance as it safeguards power stability when digital components are operational. For those embarking on high-speed design endeavors and seeking to curtail PDN impedance, a set of directives and analytical methods have been compiled. These guidelines and techniques aid in comprehending PDN impedance and its impact on maintaining power integrity.
Overview of PDN Impedance Analysis
Within a PCB's PDN, impedance is shaped by various components. At zero frequency, impedance embodies DC resistance, determined solely by the conductivity and layout of all PDN conductors. Beyond DC, impedance takes on a complex frequency-domain curve due to intricate conductor geometry. Similar to high-speed interconnects, a PDN's impedance defines interactions with electromagnetic fields.
Power integrity and test engineers approach PDN impedance analysis via two main avenues:
- Simulation-Driven Design: PDN, with its intricate parallel planes and capacitors, resists manual impedance calculations. Instead, Maxwell's equations in PDN are solved using field solvers to directly compute impedance.
- Measurement Approach: While PDN impedance can theoretically be measured, the process differs from direct transmission line impedance measurements. Instead, PDN impedance is derived from standard measurements.
When a component within the PDN undergoes state transitions, it injects current bursts during switching events. Like systems featuring reactance, this can induce oscillating voltages across PDN components, influenced by the PDN transfer function and impedance spectrum. Near-field probes or oscilloscopes can detect complex underdamped oscillations in PDNs. The accompanying graph exemplifies voltage-driven oscillations in a PDN, followed by transient decay:
The graph depicts current surges from a switching digital component into the PDN and the resultant voltage on the component's power rail (termed PDN ringing or power bus ripple). When component switching ceases, transient decay occurs, restoring the nominal DC voltage. Impedance governs how the drawn current waveform generates downstream integrated circuit voltage fluctuations, akin to the responses seen in RLC circuits.
Typically, measuring such waveforms isn't routine. Instead, impulse response measurements ascertain PDN impedance. A test signal is directed to the PDN's feed port, and the system's impulse response is gauged elsewhere on the power bus. These waveforms enable direct PDN impedance calculation, irrespective of the source signal determining PDN impedance.
Illustration of PDN Impedance Spectroscopy
When observing the impedance spectrum of an actual PCB outfitted with an assortment of decoupling capacitors, a multifaceted curve spanning the frequency spectrum emerges. The diagram below highlights pivotal contributors.
Within this illustration, the spectrum features distinctive peaks and valleys shaped by the PDN's conductor configuration, planar capacitance, dimensions, and inherent self-resonance of decoupling capacitors. Additionally, load capacitance and parasitic inductance within the PDN exert notable influences.
Determining PDN Impedance through Measurement
While the aforementioned spectrum can be gauged using a network analyzer, real-world PCBs aren't tailored for such assessments. Instead, time domain measurements must be employed to deduce the impedance spectrum within the frequency domain. Expressing it in terms of Fourier transform, the following equation encapsulates the PDN impedance in the frequency domain:
In simpler terms, by capturing voltage fluctuations and current waveforms through measurements, you can convert them into the Fourier domain and then divide them to obtain the impedance spectrum. This resultant spectrum can then be juxtaposed with the intended PDN impedance for analysis.
Comparing to Desired Impedance
In essence, we can quantify the desired impedance for a PDN by considering its maximum peak-to-peak supply voltage fluctuations and peak-to-peak current pulses:
The peak-to-peak voltage fluctuation can be as minimal as 2% for logic levels of high-speed components, or as slight as 24 mv peak-to-peak for components operating at a 1.2 V core voltage (a prime example being FPGAs). Once the actual PDN impedance is determined, it can be evaluated against the intended PDN impedance to gauge if any adjustments to the PCB layout are necessary.
A common method to compare the measured PDN impedance against the target impedance involves utilizing the L2 norm:
You can employ similar mathematical techniques as used in comparing two S-parameter measurements. Based on the above, you can assess whether the measured impedance aligns with the target impedance using impulse response measurements. Notably, this assessment is framed in terms of finite bandwidth, as the sampling interval used to capture voltage and current measurements (e.g., via an ADC) is inherently finite.
Enhancing Precision with Field Solver Tools
In summary, our exploration of PDN impedance involves experimental measurements approached from two vantage points:
Firstly, in the time domain, where we analyze the impulse response by convolving it with the PDN impulse response function.
Secondly, in the frequency domain, we delve into the signal conversion, specifically how the input current spectrum transforms into the output voltage fluctuation spectrum observed at the receiver.
Both these aspects yield valuable insights as they directly inform measurements, aiding our comprehension of the PDN impedance in the final board configuration. However, without the aid of a field solver, gaining a comprehensive understanding of how various elements within the PDN impact its impedance becomes a challenge. The most effective electromagnetic field solver tools seamlessly integrate into your PCB design software and construct accurate numerical simulations directly from your PCB layout. With such software at your disposal, you can compute PDN impedance, network parameters, and transient behavior, thus refining your analysis.
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