Ripples arise while characterizing devices at RF and microwave frequencies. RF engineers need to make sure that measurement set-up is properly calibrated and matched in order to avoid measurement errors due to ripples. Unmatched and improper interconnects, cables, connecters, SMA launches, and so on, in the set-up cause ripples that lead to measurement errors in device performance parameters, such a gain, output power, OIP3, return loss, and OIP2. Impedance mismatch within the cable, evaluation board traces, and package cause multiple reflections of electromagnetic fields, resulting in the formation of ripples. Thus, for RF device characterization, care is taken with proper measurement set-up to minimize such errors. Readers will gain a detailed understanding of theoretical analysis behind the formation of these ripples in this report. Also, lab measurements supported by some basic simulations are discussed.
Sometimes ripples are seen during RF device parameters characterization such gain, linearity, and return loss. These ripples arise due to multiple reflections of the signal travelling within cables, connectors, evaluation board traces, device under test (DUT) and package. These ripples are caused due to impedance mismatch at the junctions of these interconnects.
Figure 1a shows a basic transmission line with source VS
, source impedance ZS
, transmission line characteristic impedance ZO
load impedance ZL
. In order for an input incident wave to travel completely, the transmission line should be matched to source and load, for example ZS
= 50 Ohms. If the transmission line, which could be a co-axial line as shown in Figure 1b or microstrip line as shown in Figure 2b, has characteristic impedance not equal to 50 Ohms, then there will be reflection at the planes of mismatch. This plane of mismatch could be considered as a boundary of two mediums with different dielectric properties. The portion of transmission line where characteristic impedance is not equal to 50 Ohms could be represented as medium with absolute permittivity ε2
, and the 50 Ohms source and load could be represented as medium with absolute permittivity ε1
(Figures 1d and 1e).
Reflections due to impedance mismatch can better be understood by looking into electromagnetic wave interaction at the impedance mismatch planes. The interaction of the electromagnetic wave at these planes leads to the reflection and transmission of waves at the boundary of medium, which is quantized in terms of reflection coefficient Γ
and transmission coefficient τ
, respectively. Reflection coefficient is the ratio reflected Er
and incident Ei
electric field strength. Transmission coefficient is the ratio of transmitted Et
and incident Ei
electric field strength:
These coefficients are directly related to gain, output power, linearity, and return loss. In order to understand the ripples that occur due to impedance mismatch, it is necessary to understand reflection and transmission coefficients and the interaction of electromagnetic field at the boundaries of impedance mismatch. Any reflections in these coefficients eventually will appear in performance parameter measurements.