Mastering antenna impedance measurements (at 4-10 GHz) – Volume II
From this article, you will learn about:
- Design challenge: sources of error in vector network analyser (VNA) impedance measurements and simulation models affecting the matching circuit synthesis and verification
- Step-by-step example for the impedance measurement and verification methods recommended for the frequency ranges above 4 GHz
Introduction
Our previous blog article covered impedance measurement calibration for the design problems below 4 GHz. Our conclusions included two recommended methods, Port extension and On-board calibration, that demonstrated strong alignment between measured and simulated results within the frequency range. However, the logical question after mastering the measurements below 4 GHz was:
In this article, we focus on impedance measurements within the 4 – 10 GHz frequency range, which encompasses a variety of interesting applications.
Why 8 GHz is harder than 2 GHz?
We can identify several factors that contribute to uncertainties of matching circuit simulation models, thus causing modelling errors and eventually discrepancies between the measurement and simulation. We can readily study the influence of the following:
Factor 1): Ideal versus library component models
When we consider typical 0402 or 0201 package size chip capacitors/inductors, Factor 1) becomes a dominating source of error when going from 2 GHz to 5 GHz and higher. As an example, we simulate the S11-response of an antenna with a matching circuit assuming (a) ideal component models and (b) using library component models with the same nominal values as in case (a).
The matching circuit design target is a dual-band response at 5.5 GHz and 7 GHz. The difference between (a) and (b) deviates strongly above 3 GHz. It is interesting to look at the difference |S11,ideal – S11, library| over frequency, Figure 2, where the difference is measured as the distance between the S11 values within Smith chart. A difference of 0.1 can be considered small, and in this example the corresponding upper frequency limit is 3.13 GHz. The difference increases rapidly at higher frequencies, reaching 0.5 (half the radius of Smith chart) at 4.2 GHz. This study is one explanation why the use of vendor library models can be somewhat relaxed below 3 GHz, but must absolutely be used at 5 GHz or above.
Figure 1: Simulated S11-response of a matched antenna using the same matching circuit, but assuming ideal components (blue curve) or using vendor library component models (green curve)
Figure 2: Absolute value of the difference between complex reflection coefficients assuming ideal components or vendor library component models
Factor 2): Non-ideal grounding of shunt components
In a typical scenario the shunt component ground is not exactly equal to the signal ground. The top ground layer is usually nailed by vias to the ground layer below the signal trace, and thus there is an inductive return current path from the negative terminal of the shunt component to the signal ground. As a rule of thumb, one may expect inductive grounding in the range of 0 – 0.2 nH, which may sound small, but let’s look at its impact closer.
Motivated by the findings of Factor 1), we re-design the matching circuit using library component models for a dual-band response at 5.5 GHz and 7 GHz. We then check the impact of additional 0.2 nH inductance to the shunt components, Figure 3. We observe a big impact, Figure 4.
Figure 3: Dual-band matching circuit, with 0.2 nH extra inductance added to the shunt component simulation model
Figure 4: Comparison of matched antenna response assuming ideal versus inductive grounding of shunt components
However, it is not true that assuming 0.2 nH extra shunt inductance always has such a big impact, even if the frequency is high. Therefore, we cannot state a general rule here, but it is easy to check the hypothetical impact, and if it is significant, be prepared to adjust the simulation model as described shortly.
Factor 3): Uncertainty of reference plane location
Even a carefully calibrated measurement involves some uncertainty regarding how well the effective reference plane agrees with the first matching component model’s reference plane. This may cause big enough phase rotation that makes the matched response to deviate far from the target. Figure 5 illustrates the phase rotation due to 1 mm shift of the reference plane, causing 40 degree rotation at 8.5 GHz. If we assume zero shift in the reference plane, but if there is 1 mm shift in reality, the optimized matching circuit works poorly.
Figure 5: Unmatched antenna S11-response with and without assumption of 1 mm shift of the reference plane. Marker at 8.5 GHz.
Factor 4): Matching circuit component interconnects have non-zero size
Optenni Lab offers two methods to model the board layout of the matching circuit: EM-simulated Layout block or a simplified model based on transmission line segments. While Layout block can model arbitrary geometries covering also shunt grounding issue of Factor 2), if the layout is a simple chain, a simplified model often provides sufficient accuracy. Further benefit of the simplified model is that its dimensions can be optimized. Therefore, uncertainties related to component models’ effective reference planes can be absorbed in these dimensions.
The interconnect dimensions have a big effect to the matching circuit operation, as is demonstrated in Figure 6.
Figure 6: Comparison of matched antenna response assuming ideal versus finite connectivity between the matching components
Factor 5): Signal transition inductance from measurement pigtail onto the signal line
When a pigtail is soldered on the board, the signal experiences a discontinuity when it exits the coax shell and propagates down the transmission line towards the antenna. Typically, this discontinuity is equivalent to about 0.5 nH lumped inductance. This inductance is present in the measured impedance but not when the device is operational. Therefore, if the impedance is not corrected for this inductance, we are introducing an error to the matching circuit design input data. Once again, the impact may be significant as illustrated in Figure 7.
Figure 7: The green curve shows the S11 response if there is 0.5 nH signal transition inductance in the measurement of the unmatched antenna, while the blue curve represents the designed response omitting this inductance
To summarize, each
of the Factors 1)-5)
can have a big
impact on the success
of the matching circuit
design, explaining
“why 8 GHz is
harder than 2 GHz”.
In the following chapter we explain how to bring all these factors under control so that we can design a working matching circuit also at high frequencies.
How to bring all these parasitics under control?
There are two keys to success in this matching challenge. The first is the use of accurately calibrated pigtails. Optenni partners with Dicaliant Ltd, who delivers calibration kits and compatible measurement pigtails for frequency categories from 4 GHz up to 8.5 GHz. The second key to success is to follow a sequential measurement-modeling sequence. The method incrementally improves the model accuracy, and the design target is typically achieved on the first attempt or in just one iteration. We will consider this sequence next.
Step 1: Measurement of open-ended short segment of feedline
It is a useful checkpoint to begin by measuring only the matching circuit layout section such that all shunt components are unpopulated and all series components shorted, except the one closest to the antenna, see Figure 8.
Figure 8: Suggested first measurement step
This step serves several purposes: it validates quantitatively the RF grounding of the feed line (does the response look like that of an open-ended transmission line?), it characterizes the substrate (how many degrees phase delay there is for X mm of the line), and it characterizes Factor 5) above, the pigtail landing inductance. In practise, a simple model is fitted to the measured response, which is then very easy to de-embed from the subsequent measurements, see Figure 9.
Figure 9: Example circuit resulting from model fit to measured open-ended transmission line segment
Step 2: Measurement of unmatched antenna
In the second step, the remaining series component gap is also shorted, and thus we are measuring the impedance of the unmatched antenna. The pigtail is not moved, so the parasitic landing inductance is the same. By de-embedding the model of Figure 9 from the result takes the calibration reference to the first matching component closest to the antenna, to be compatible with Optenni Lab synthesis. The de-embedding can be done explicitly in Optenni Lab by adding a negative inductance and negative length transmission line in series with the measured antenna data (note the flipped order of components, subtract inductance first). The de-embedding causes a counterclockwise de-rotation of the S11-trajectory in Smith chart, Figure 10.
Figure 10: Unmatched antenna S11-response before and after de-embedding of the transmission line segment from pigtail tip up to the first matching component
Step 3: Synthesize, implement and measure a matching circuit
Next step is to use Optenni Lab to synthesize a candidate matching circuit. You can already include a coarse interconnect model between the matching components. This partly tackles Factor 4), and use of vendor component libraries in the synthesis tackles the most important Factor 1) in the list of error sources. The synthesis is carried out typically using generic reactance components in Optenni Lab, providing multiple optimized topologies in one go. Figure 11 shows the simulation vs measurement for the resulting first candidate circuit (synthesis carried out with library components for generic reactance components). We observe a noticeable difference between the simulated and measured result.
Figure 11: Simulation vs measurement of the 5.5/7.0 GHz dual-band design (above), first candidate circuit (below)
Step 4: Adjust the simulation model to fit measured response
There are still several nonideality factors that we can cover in a single adjustment step. First, to account for Factor 3), uncertainty in the reference plane location, we add an optimizable transmission line with zero nominal length, and optimization length range including negative and positive values. This allows moving the reference plane towards antenna or away from it. Second, to account for Factor 2), the non-ideal grounding of shunt components, we add inductances of zero nominal value to the shunt components, with optimization limits of 0 – 1 nH. Third, to improve resolution of Factor 4), we optimize the length of the interconnect models between components.
The optimization target for the simulation model is to find parameters which make the simulated S11 agree with the measured S11 over the whole measured frequency range. A successful model fit is indicated by the cost function value of -2.0 or higher, and for example cost = -1.0 is considered an excellent fit. Please note that to compare apples to apples, we must include the pigtail landing inductance in the simulation model. In this example, we reach a good model fit with cost = -1.8.
Step 5: Re-optimize the component values to meet the target
If the layout model fit is good, we have the physical response under control. Fixing the layout model and re-optimizing the component values, often a single iteration is enough to reach the target. In our example, two iterations were needed, mainly because the higher resonance is very sensitive, but the resulting simulation vs measurement agreement is really good, Figure 12.
Figure 12: Simulation vs measurement after re-optimization of the component values. Coarse component value grid in the capacitor library prevents exact tuning of the higher band of the example antenna to 7.0-7.2 GHz.
Conclusions
We have discussed many roadblocks that hinder simulations to agree with measurements, especially when dealing with matching circuit design above 5 GHz. There are two things required for smooth design success: an accurate pigtail calibration kit, and a careful modelling-measurement sequence. The checkpoints in the process provide a possibility to review the prototype or simulation model early. Following these principles often provides a satisfactory result, even on the first attempt or after just one adjustment iteration.
Account Manager
jaakko.juntunen (at) optenni.com
