*Paul Tornatta, VP RF Systems and Antenna Engineering*

*Cavendish Kinetics, Inc.*

Modern Smart Phones are packed with useful features. In order to maximize the user experience, the performance of the radio must be optimized at all times. Antenna Aperture Tuning is a method used by all top-tier Smart Phone makers for optimizing the antenna performance across several frequency bands of operation. The next step in antenna optimization is closed loop tuning. In closed loop tuning, some performance metric (often antenna reflection coefficient) is used to change the response of the RF front-end to dynamically compensate for variations in usage including compensating for the detuning effects of the users head and hands during phone operation. Dynamic tuning to compensate for head and hand effects is not a new concept. Most RF engineers believe the best way to implement closed loop tuning is with an impedance matching network, but if aperture tuning, not impedance matching, is the best way to tune an antenna, then why not use aperture tuning for closed loop tuning as well?

Optimum aperture tuning requires a tuner with special characteristics including low equivalent series resistance, low minimum capacitance, and tolerance to high voltage. MEMS based variable capacitors from Cavendish Kinetics have all of these characteristics. In addition, they also have 5-bit control giving 32 capacitance states. With the MEMS variable capacitor already in the phone being used for band select and channel tuning, it’s just a matter of applying the right software to turn it into a closed loop tuner as well.

Aperture tuning is the best method for antenna tuning and therefore the best method for closed loop tuning as well.

**The Problem
**There are three main contributors to loss due to the changing environment around the antenna during phone operation; absorption loss, impedance mismatch loss and antenna resonance efficiency loss. Total losses can be as high as 12-15 dB (1). The main loss mechanism is absorption loss accounting for 8-10 dB loss. Other losses include impedance mismatch losses accounting for 1-2 dB, and antenna radiation efficiency loss accounting for another 2-3 dB of loss. Nothing can be done to recover absorption loss, however, impedance mismatch and radiation efficiency loss can be recovered by changing the resonance of the antenna. This is exactly what aperture tuning accomplishes.

As stated earlier, dynamic tuning to compensate for head and hand effects is not a new concept. It is well known that the users hand and head or other objects can cause the antenna resonant frequency to shift. This effect is primarily capacitive loading and primarily affects the low frequency bands of operation (2). When the antenna resonant frequency shifts, the impedance it presents to the rest of the radio front end shifts away from an optimum value causing an impedance mismatch. This mismatch has three main effects; more energy is reflected from the antenna terminals rather than passing through the terminals, the output power from the power amplifier (PA) drops due to load pull, and the antenna radiation efficiency is reduced due to capacitive loading. Existing implementations of dynamic closed loop tuning focus on reducing the mismatch between the antenna and the PA to optimize the power transfer.

This technique requires monitoring both the magnitude and phase of the forward and reflected power at the terminals of the antenna effectively measuring the antenna impedance in real time. As the antenna impedance changes due to the loading affect of changes in the environment, the impedance information can be used to synthesize a conjugate match or to select a “best match” from a lookup table. The new antenna matching state is then loaded into a complex variable matching network located at the antenna feed point. This then improves the power transfer through the antenna terminals and reduces the impact of power amplifier load pull. Figure 1. shows a simplified block diagram of a conventional impedance match closed loop tuning system.

This technique of closed loop tuning has several drawbacks. In order to measure antenna impedance, both the magnitude and phase of the reflection coefficient must be known. Once the magnitude and phase are known, a conjugate match must be synthesized requiring significant computational cycles and time. A lookup table can reduce the time significantly at the expense of accuracy. In order to implement a complex match, a complex matching circuit is required. While this overhead is beneficial for the frequency band that is being compensated, typically the low band, it contributes loss to all other frequency bands of interest. Losses at high frequency bands can be significant (>1 dB). Finally, this technique only compensates for impedance mismatch recovering 1-2 dB of loss. This technique does not restore the energy lost due to the reduction in radiation efficiency of the antenna structure. Using an impedance matching network to compensate for head and hand loading can introduce enough loss to overcome the benefit.

**The Solution
**A better solution is to use the existing aperture tuned antenna to compensate for head and hand effect. As with the impedance matching technique, the reflection coefficient is measured at the antenna feed terminals. This information is used to select a new tuning state for the antenna to optimize the resonant frequency of the handset in the new loaded condition (phone + hand + head). This technique not only restores 1-2 dB of performance lost due to impedance mismatch, it also restores 2-3 dB of loss by improving the antenna structure radiation efficiency. The total benefit of this technique is 3-5 dB compared with 1-2 dB from the impedance compensation alone. Figure 2. shows a simplified block of closed loop tuning using an aperture tuned antenna.

Two key factors are required for an aperture tuned antenna to be used in a closed loop tuning application. First, the tuner must have a large number of closely spaced tuning states. This allows the resonant frequency to be shifted by small amounts with minimal risk of call drop. Second, the reflection coefficient vs. frequency must be mapped into reflection coefficient vs. tuner state. Holding frequency constant and varying capacitance yields the same characteristic curve as holding capacitance constant and varying frequency. So reflection coefficient measured at a single frequency with varying tuner state can be used to find a minimum reflection coefficient and therefore optimum tuner state, for any loading condition.

**Four Techniques For Using Aperture Tuned Antennas for Closed Loop Tuning
**The first three techniques are scalar techniques and involve monitoring only the magnitude of the reflected power at the antenna terminals using a simple directional coupler. The fourth technique uses both the magnitude and phase of the reflection coefficient to solve directly for the tuner setting required to restore the antenna resonant frequency.

**Technique 1: Least Squares Fit
**This technique can be run at any time during normal phone operation. It can be triggered by an event, like an accelerometer, gyro or grip sensor. It can also be time triggered or triggered by plugging in a USB or audio cable. Once the algorithm is triggered, the magnitude of reflection coefficient is measured at the initial tuning state (S

_{i}) at a single frequency in the transmit band. Then at S

_{i}+1 and S

_{i}-1, at the same frequency. These three tuning states are used to determine if the slope of the reflection coefficient vs. capacitance is positive or negative.

Three more reflection coefficient measurements are made moving down (toward lower reflection coefficient) the slope of the curve. Moving down the slope insures that the call will not drop as the tuner state is changed. After measuring six data points, a least squares fit algorithm is run to find the best fit parabola to the data. The tuning state that represents the vertex of the parabola is compared to the initial tuning state. The difference between these two states is the number of states that must be moved to retune the antenna to optimum performance. Figure 3. Illustrates how this technique works and shows the initial tuning state and representative reflection coefficient vs. capacitance curve, the newly computed reflection coefficient vs. capacitance curve, and the resultant curve for the new optimized capacitance setting.

**Technique 2: Threshold Tuning with Upper Control Limit
**This algorithm can be triggered to run in the same manner as the Least Square Fit algorithm. Once triggered, the magnitude of the reflection coefficient is measured at a single frequency in the transmit band to see if it exceeds a predetermined upper limit. If the limit is exceeded, the tuning state is increased by one and another measurement made. If the new measurement is higher than the initial measurement, the algorithm will “turn around” and decrease the tuner state. If the new reflection coefficient still exceeds the threshold limit, the algorithm continues to decrease the tuner state until the reflection coefficient is less than the threshold limit. Then the algorithm stops. It can be triggered again by another event at a later time.

** Technique 4: Trough Detection
**This algorithm is designed to run continuously and maintains the reflection coefficient at the minimum value at all times. It does not contain upper or lower threshold limits. The algorithm starts with an initial tuner state the alternately increases and decreases the tuner state to determine a positive or negative slope of the reflection coefficient curve. The algorithm moves in the direction of decreasing reflection coefficient by one state and repeats the measurements. In this way, the tuning state of the antenna is constantly being adjusted toward lower reflection coefficient.

** Technique 4: 3-Point Direct Vector Algorithm
**Just as in techniques one and two, this technique can be triggered at any time or by any event. It requires measurement of complex (magnitude and phase) reflection coefficient at a single frequency for three different tuner states. With this data, the complete S-parameter matrix solution for the antenna structure can be computed. Once the S-parameter matrix is known, reflection coefficient vs. capacitance over all tuning states can be computed.

The tuner setting for the minimum value of reflection coefficient is the new tuner state required to optimize the antenna radiation efficiency. This technique takes advantage of microwave circuit theory and works on the principal that the antenna structure is a two-port device with Port 1 (P1) being the feed point and Port 2 (P2) being the connection to the tuner. The reflection coefficient at P1 can be measured and the reflection coefficient at P2 can be calculated from the frequency and the tuner state. The terms of the S-parameter matrix are a function of the reflection coefficient at P1 and P2. A system of three equations with three unknowns can be set up from three reflection coefficient measurement at three different tuner states all measured at the same frequency. Figure 4 shows the S-parameter configuration for the antenna as a two-port device.

**Conclusion
**Antenna Aperture Tuning to optimize antenna performance across multiple frequency bands is common in Smart Phone architectures. It is possible to use the existing antenna tuning hardware to implement dynamic closed loop tuning to further improve Smart Phone performance by compensating for the loading affects of the user and environment. Aperture tuning improves the radiation efficiency of the antenna system while simultaneously improving the power transfer at the antenna terminals. The combination of which can improve system performance by up to 5dB.

As stated earlier, aperture tuning is the best method for antenna tuning and therefore the best method for closed loop tuning as well.

*For more information visit www.cavendish-kinetics.com*

*1) “Analysis and Optimization of Mobile Phone Antenna Radiation Performance in the Presence of Head and Hand Phantoms” – Ofli/Kuster et al; SPEAG & ETH, Switzerland, 2008*

*2) “The Effect of the User’s Body on High-Q Planar Inverted F Antennas for LTE Frequencies”; Pedersen et al; University Aalborg, Denmark, 2012*