Ultra-Low PDN Impedance Measurements Using 2-Port VNAs

Introduction 

In this application note, a 2-port network analyzer is used to measure impedances well below 1 Ohm. This regime is difficult to measure in practice with a conventional 1-port VNA due to real-world limitations of signal-to-noise ratio and fixturing reproducibility. With this new technique of using 2-ports and a conventional network analyzer, impedances as low as 1 milliOhm and inductances in the pH range can be routinely measured. This type of measurement is critically important for all the components that make up the power distribution network system.

Table of Contents: 

• Limitations of 1-Port VNA Impedance Techniques
• 4-Point Kelvin Technique for Ultra-Low DC Resistance Measurements
• 2-Port Measurements Reduces Fixturing Parasitics
• Measurement Examples Using the Two-Port Measurement Technique 
• The Power Distribution Network (PDN)
• Decoupling Capacitors
• Planes and Capacitors 
• How to Set Up a Measurement System
• Conclusion

Why is low impedance important? 

Most interconnects used to transport signals have impedances in the 50 to 100 Ohm range. This is in the perfect range for measurement by conventional network analyzers with port impedances of 50 Ohms. But, for structures with ultra-low impedances, the mismatch with the 50 Ohm source impedance means that nearly all of the signal will reflect, and distinguishing 0.1 Ohm from 0.01 Ohms becomes extremely difficult. It is predominately in the power distribution network (PDN), the interconnects from the voltage regulating module (VRM) that generates the precisely regulated voltage to the pads on the chip for the Vcc or Vdd rails, where ultra-low impedance values are required. It is not uncommon in microprocessor-based systems to have a target impedance for the entire PDN of less than 10 milliOhms from DC to a few GHz. Each of the components that make up the PDN, the package leads, the ceramic capacitors, the on-chip capacitance, the power and ground planes of the circuit board, and even the VRM itself, must have impedances in the milliOhm range. It is not practical to measure them with the conventional return loss of a 1-port VNA, these are the sorts of applications for which the 2-port technique is critically important. 

• Vias
• Package attach elements: wire bonds, solder balls
• Ceramic capacitors
• On-chip capacitance
• Planes
• Power distribution networks
• Voltage regulator modules (VRM)

Limitations of 1-Port VNA Impedance Techniques

The simplest equivalent circuit model for 1-port of a VNA is a sine-wave generator with a source impedance of 50 Ohms. This signal transmits through an internal 50 Ohm coaxial transmission line to the front connector of the VNA and is launched into the device under test (DUT). The amount of the incident sine wave which comes back to the detector and is measured as the reflected signal depends on the miss-match in impedance between the DUT and the 50 Ohm source. The reflection coefficient, S11, is the DUT impedance minus the 50 Ohms, divided by their sum. You can use this relationship to estimate the value of S11 for low impedance devices.

When the impedance of the device is 1 Ohm, S11 is –0.96 or –0.35 dB. This is a reasonable value to be able to measure. When the impedance is 0.1 Ohm, S11 is –0.996 or –0.035 dB. This may seem like a very small amount of reflected signal, but in fact, 99.6% of the incident signal reflects. This is so close to 100% that it is difficult to measure the difference between 100% of the signal and 99.6% of the signal. This creates a large relative uncertainty. 

When impedances are less than a small fraction of an Ohm, the magnitude of the reflected signal is so close to 1 that it is difficult to distinguish it from 0 Ohms. This is a fundamental problem.