High speed printed circuit board (PCB) design requires well designed power delivery networks (PDN) to support today's FPGAs or custom mixed-signal ASICs. The PDN contains important impedance information that can offer the designer insight into how a system will react to dynamic currents. The PDN is the transmission line connecting the voltage regulator module (VRM) and the load, making the VRM a good starting point for a successful PDN design.

Vendor information for a VRM’s output impedance is not always provided, and when it is provided it may not be accurate. Further, measuring ultra-low impedance on multiple VRMs, or a multi-topology DC-DC regulator, is a challenge for many design engineers. The 2-port shunt-through measurement is the gold standard for measuring a VRM’s output impedance in the milliOhm and sub-milliOhm region [1]; however, it is not always possible to make these measurements without including dedicated RF connectors on the PCB or device under test (DUT). Therefore, when a designer makes these types of measurements with a vector network analyzer (VNA), the method of connecting the DUT requires attention to detail to ensure inductance is minimized to allow an accurate measurement.

Without dedicated RF connectors, it’s common to use a pair of 1-port microprobes with probe positioners, or a probe table. Although this connection method works quite well, it is not the most convenient, particularly if a system has many VRMs that need to be measured. Picotest tried to address this issue by developing a hand-held probe that contained both ports in a single head. Due to manufacturing constraints, the probe only included a single ground pin. Without 4-point contact at the DUT, contact resistance significantly limited the impedance the probe could measure; however, in general (not specific to this 2-port probe) both inductance and contact resistance limit the impedance measurement. The minimum measurement recommendation for the P2101A probe is 25 mΩ. Many, if not the majority of VRMs today, present lower impedance than 25 mΩ.

Recently we reviewed a pre-production prototype of the new P2102A 2-port browser probe from Picotest. This browser probe includes 4 probe tips to allow measurement across a variety of SMD packages on a PCB, such as 1206, 0805, 0603, or 0402. The P2102A probe tips are available as 1X, 2X, 5X, and 10X.

We evaluated the 2X version, which includes 50 Ω series resistors (Rs), allowing higher voltage and reduced loading on the DUT, but it also raises the impedance floor. As some measurements were being done on some VRMs, we hypothesized: “At what point with this probe does the mutual inductive coupling in the probe tips during a 2-port browser become a factor that impacts our measurement without proper calibration?”

Thinking back to our undergraduate EE class on electromagnetics or physics, the mutual inductance can be described by Maxwell’s equations and Faraday’s law. More simply, from Faraday’s law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) or voltage in the conductors [2]. This relationship for mutually inductive wires is shown by equation (1).

                             

In short, mutual inductance can lead to crosstalk between the two probe tips during 2-port measurement, causing error. Higher frequency means higher di/dt, so the noise due to the coupling increases with increasing measurement frequency. This can be represented as an extraneous inductance.

Brian Hostetler at Cray (now HPE) gave us a simpler way to think about this: “Mutual inductance creates a path for current to jump from one probe to the other without going through the DUT. This ‘shortcut’ current results in a voltage at the receiving probe. The isolation calibration records this voltage and subtracts it from all future measurements.” Brian is saying that when looking at other calibration methods with isolation, we are taking into account more terms to allow better error correction. 

With reference to an EDICON 2018 presentation titled 100µΩ Probing Methods [3], the equation for mutual inductance between two wires can be found by equation (2). Where k is the coupling coefficient that varies between 0 and 1.

Let’s step back for a moment to understand the purpose of calibration and why it is important with any VNA. Proper calibration increases the accuracy of measurements on a test setup by correcting for errors from the cables, probe contact resistance, probe tip inductance, and coupling effects. Unfortunately, other effects such as thermocouple effects and contact resistance are time varying. In this 2-port probe example, the 4-point probe contact resistance is the primary variable that affects the common mode rejection ratio (CMRR) which impacts measurements at the lowest frequency. This is primarily due to the fact CMRR typically deteriorates at higher frequencies. The key to achieving good calibration is related to moving the test setup’s reference point as close as possible to the DUT.

From a standards perspective, one of the most common calibration methods is the SHORT-OPEN-LOAD-THRU (SOLT); however, not all VNAs support this calibration method. Another common 2-port calibration method is the SHORT-OPEN-LOAD (SOL), which is available on the OMICRON Lab Bode 100. The Bode 100 is a frequency response analyzer (FRA); however, any FRA that measures both magnitude and phase is also technically a VNA. As previously mentioned, there is also isolation calibration that can further minimize the effort of inductive coupling. This calibration is available on other VNAs from Copper Mountain Technologies, Keysight, and Rohde & Schwarz.

When it came time to calibrate the setup with the Bode 100, there were two options available for this VNA: 1) the Thru-Calibration method; or 2) the SOL calibration. When measuring impedances in the milliOhm region with a VNA like the Bode 100, the SOL calibration method is much more accurate.

The shunt-through measurement configuration, shown below in Figure 1, inherently suffers a ground loop error at low frequencies. The current flowing through the cable shield of the connection to channel 2 ground introduces a measurement error that can show up at all frequencies; however, the error typically becomes the most significant at lower frequencies (typically below a few MHz) when measuring very low impedance values. This is primarily because the cable outer connectors are in parallel with each other and in series with the DUT.

Fig. 1 - 2-port shunt-through with series resistance impedance measurement setup using Bode 100 and Picotest ground isolator J2102B.

To reduce the ground loop error at low frequencies, use a common mode choke, common mode transformer, or an active isolation device. This method has been demonstrated with simulation tools such as Keysight Pathwave ADS and, as an example, is shown in Figure 2 below.

Fig. 2 - 2-port shunt-through measurement modified by the addition of a series resistor at each VNA port [4]. 

Also keep in mind that the inductive coupling between the two sets of tips depends on how much the tips are pressed down or compressed on the DUT. Further, different tips will have different inductive coupling. With that being said, during calibration a probe holder was used to ensure consistent tip pressure as best as possible, as shown in Figure 3.

Fig. 3 - Measurement Setup after Calibration with Bode 100.

Using a TDR, the probe tip inductance and capacitance can also be found, which is demonstrated by Figure 4 [5].

Fig. 4 - TDR Measurement of P2102A-1X - 0805 Probe Tip.

With reference to Figure 4 the inductive blip measured with a TDR can be calculated by equation (3) [5].

In this case, where R_ref = 50Ω, the reflection is the area of the blip found through integration using the math functions on the oscilloscope, L = 2.6 nH. Note that just to the left of the left cursor in Figure 4, there is another small bump, which is also an inductor. The sum of those two inductors adds up to 3.1 nH.

As shown by the ADS workspace example in Figure 5, this information can be further used to export a touchstone file that can de-embed the probe tip prior to measurement on a respective VNA.

In Figure 5, The inductance (Ltip) was measured using a TDR and the coupling term (K) was measured from crosstalk by shorting the probe tips. The probe capacitance, C1, was found by tuning to match the OPEN probe measurement. This is a relatively unimportant term since we are measuring low impedance instead of high impedance, but just like there is an inductive residue due to the inductive coupling, there is also a capacitive residue due to the capacitive coupling. For completeness, C1 is included. The data was then manually fine-tuned in ADS to match the OPEN, SHORT, and DUT probe measurements compared with the SMA connector measurements.

Fig. 5 - ADS Schematic P2012A-1X 0805 Probe Tip.

Analysis

For reference, Figure 6 provides a depiction of the calibration substrate points used for SOL calibration method with the Bode 100, whereas Figure 7 provides a depiction of the point used for the thru-calibration method. The center image in Figure 6 is also the short test point measured as shown in Figures 8 and 9. Regarding the calibrating load, all the resistors on the calibration substrate shown in Figure 6 are 1005 package size at 49.9 ohms.

Fig. 6 - P2102A 2-port SOL Calibration Points with Bode 100 - Open (left), Short (center), and Load (right).

Fig. 7 - P2102A 2-port Thru-Calibration Point with Bode 100.

After performing a thru-calibration for each probe tip then measuring the short on the calibration substrate, we can observe from ~100 Hz to 3 kHz a falling slope which is indicative of resistance in the ground, mostly from the ground pins, and the inductance of the common mode transformer. The resistance of the ground pin varies with compression. These effects are not being corrected with the thru-calibration method; however, after ~100 kHz, we see the curve become inductive. This is the mutual inductance that is seen by each probe tip, in addition to a certain amount of inductance that is present, defined by the spacing of the probe tips.

With reference to Figure 8 and Table 1, at 10 MHz (Cursor 3), we observe that there is a 107 mΩ inductive impedance difference between the 0402 probe tip and the 1206 probe tip. If we approach this change in impedance logically, we know the inductance of these four probe tips are not all equal due to the length differences in each tip and due to the tip physical distance discussed above. From this we can observe a change in impedance between each of the four probe tips. Again, we can clearly see the effect of the mutual inductance that is created by these different probe tips when using the thru-calibration method for measurement.

Fig. 8 - Thru-Calibration Method - Short Impedance Measurement for P2102A-2X Probe Tips on Bode 100.

Table 1 - Results Summary - Thru-Calibration Method - Short Impedance Measurement for Probe Tips.

Based on the results shown above, in Table 1 and equation (4), we can calculate the mutual inductance at 10 MHz seen for each probe tip. These calculations are shown in Table 2.

Table 2 - Probe Tip Mutual Inductance.

Lastly since the 1206 probe tip leads are the furthest apart, it makes sense that you would see the largest inductance for this probe tip in comparison to the other probe tips. In other words, the 1206 probe tip has the largest inductive loop.

Now let’s take a look at all 4 probe tips after each has been calibrated using the SOL method with the Bode 100. With reference to Figure 9 below, we see a much flatter impedance measurement consistently around or below 1mΩ. In fact, with regards to cursors at 10 kHz, 1 MHz, and 10 MHz, we see change in impedance that is less than 0.5 mΩ (or 500 uΩ). The capacitive sloping curve seen before is also gone.

Let’s explore what changed...

During the SOL calibration, inductive coupling in the probe tip was corrected and can be observed by the flatter curve seen by all four probe tips hovering around 1 mΩ up to 20 MHz. The inductive curve appearing around 20 MHz is due to the mutual inductance in the probe as well as the finite distance between the probe tips, which also provides an inherent inductance that is not accounted for during this calibration.  Unfortunately, due to the limit of the Bode 100 being at 50 MHz, this inductance curve cannot be further explored; however, including an isolation calibration would further remove this inductive curve. This calibration will be discussed in more detail later.

Fig. 9 - SOL-Calibration Method - Short Impedance Measurement for P2102A-2X Probe Tips on Bode 100.

Table 3 - Results Summary - SOL-Calibration Method - Short Impedance Measurement for Probe Tips.