Increase range in 2-port impedance measurements
Measuring the output impedance of wideband op amps presents a formidable challenge because of their high DC gain, which results in low closed-loop output impedance at low frequencies. Above the frequency of the op amp's internal dominant pole, however, its output impedance becomes inductive. Thus, the output impedance increases at 6 dB/octave and can increase to 100 O or more at the closed-loop bandwidth frequency. Fortunately, you can overcome this problem with some simple techniques.
For the purposes of this article, we'll consider the AD8048 250 MHz, General Purpose Voltage Feedback Op Amp from Analog Devices. At a gain of 2, the output impedance graph in the manufacturer's datasheet ranges from less than 0.1 O to more than 100 O as shown in Figure 1.
Figure 1. The AD8048 output impedance graph from the manufacturer's datasheet shows a minimum impedance of approximately 85 mO, which is below the minimum limit of the 1-port measurement and a maximum impedance of 100 O at 1 GHz. That impedance is above the maximum limit of the 2-port measurement.
A summary of the impedance measurement ranges for various methods is shown in Figure 2. The impedance to be measured is within the impedance limits of a 3-port FRA (frequency response analyzer) measurement, but exceeds the frequency range of all common FRAs. The 1-port measurement can measure the impedance above 5 MHz or so and up to the 1 GHz maximum frequency, but won't provide the low frequency measurement results. Similarly, the 2-port impedance measurement can provide the impedance from low frequency up to a few hundred megahertz, at which point the impedance is greater than the 2-port technique can accurately measure.
Figure 2. The impedance measurement ranges for various measurement techniques. Note that the 3-port measurement covers the required impedance range, but not the maximum frequency, while the 1-port and 2-port measurements can accommodate the frequency range but not the impedance range, unless the impedance is measured in 2 parts.
Figure 3 shows how you can modify a 2-port VNA measurement to accommodate the necessary range. Inserting a series resistor in series with each VNA port, or replacing both VNA cables with attenuating transmission line probes results in the S21 shown in Equation 1. As with the standard 2-port measurement, DC blockers can be added to each port in order to eliminate DC loading of the DUT.
Figure 3. Simulation schematic showing the added series resistors as well as the necessary coaxial transformer. As with the standard 2-port measurement, DC blockers can be used on both ports in order to eliminate DC loading of the op amp or other DUT.
Solving Equation 1 for the impedance being measured, Rdut, results in Equation 2. You may recognize the familiar 2-port impedance transformation if Rseries is set to zero.
Inserting 450 O in series with each port or using a pair of 500 O, low impedance probes increases the impedance range by an order of magnitude allowing a measurement range of approximately 2.5 mO to 500 O. The S21 measurement results for various Rdut and series resistor combinations is shown in Figure 4.
Figure 4. S21 measurement results for various Rdut and Rseries combinations. Note that the impedance measurement range is increased with series resistance while the S21 value for a given resistance is decreased. The minimum measurable resistance is set by the signal to noise ration and dynamic range of the VNA, which are generally in the range of 100 dB.
Figure 5 shows the simulation results for the schematic in Figure 3, along with the impedance transformation equation.
Figure 5. The simulation results for the schematic shown in Figure 3 provide the correct results, despite being above the impedance range of the standard 2-port measurement.
This method also works for low power voltage references and linear regulators that span the 1-port and 2-port measurement ranges. For a review of the 2-port measurement technique see the additional references below.
Power Integrity: Measuring, Optimizing, and Troubleshooting Power-Related Parameters in Electronics Systems, S.M. Sandler
Evaluating DC-DC Converters and PDN with the E5061B LF-RF Network Analyzer
Measuring Milliohms and PicoHenrys in Power Distribution Networks, DesignCon 2000
Accuracy Improvements of PDN Impedance Measurements in the Low to Middle Frequency Range, Istvan Novak, Yasuhiro Mori, Mike Resso, DesignCon 2010
On-Die Capacitance Measurements in the Frequency and Time Domains, DesignCon 2014