Z(f) Constant Output Impedance Design
frequency applied by the application. Hence a better method is needed to extract the impedance profile with the VR operating. The following sections introduce the theory behind using a VTT tool to create an impedance profile for the VR system.
A.2 Voltage Transient Tool (VTT) Z(f) Theory
The following expression is the definition of impedance as a function of frequency looking back from the VTT tool into the filter network and VRM.
Z ( f ) = FFT (V (t))
FFT (I (t))
The representation of the corresponding Fourier spectra of the voltage and current responses are shown in Figure A-2. The first harmonic values from the Fast Fourier Transform (FFT) are used in the calculation of Z(f). The ratio of the two, yields the impedance at a given frequency, f. By sweeping the VTT generated load transient repetition rate, I(t), over the desired region of interest, additional points are estimated on the impedance profile to obtain a near continuous impedance spectrum plot.
In the VTT tool, the die voltage, V(t), is brought out through a pair of non-current carrying remote sense pins, tied to the Vcc and Vss power plane and measured on the VTT tool substrate. The current, I(t), is a differential voltage measured across the current shunt resistors in the VTT tool. The oscilloscope's math function is used to convert the time domain voltage droop and current measurements into their corresponding frequency domain spectrum. Since the FFT of the actual response waveforms are calculated, perfect square waves of current are not needed as a stimulus. The accuracy and frequency response of this method is limited to the current shunt resistor's accuracy and the shunt's parasitic inductance. Parasitic inductance in the current shunt resistors will over estimate the actual current and hence the method will under estimate the impedance at frequencies where the inductive voltage drop dominates the resistive voltage drop. The 50 pH of parasitic inductance in the VTT causes an over estimation of current for frequencies over 1 MHz and an under estimation of impedance. This can be corrected by post processing of the data and removing the inductive voltage spike.
