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Artificial neural networking (ANNs) can approximate an unknown, non-linear, multidimensional input-output mapping, once trained with an appropriate training set. The ANN output, y, is given by mapping y = y(x,w), where x represents the inputs and w the ANN parameters, or weights, that are optimized during the training process^[1].

The ANN training is done using an APLAC component, ANN model generator. The ANN model generator supports multilayer perceptrons (MLPs), which belong to a general class of ANN structures called feed-forward neural networks. An example of a 3-10-8-2 MLP ANN is shown in Figure 1. Inside each (non-input) neuron, its inputs and a bias term (not shown) of 1.0 are multiplied by a weight parameter, summed and fed to the activation function, which gives the neuron output value^[1].

The ANN training will use a set of data, called a training set, a collection of data samples, each consisting of relevant inputs and desired outputs obtained from measurements or simulations. The actual ANN training is performed by adjusting the ANN weights using any optimization method of APLAC. An independent sample set called test set should be used to verify the ANN training results. In order to create accurate models and avoid overlearning, another independent data set, the validation set, should also be used.

After the training is complete, an ANN model file is produced. This file can then be used in order to access any of the device output values as a function of any input value combination. In APLAC, the ANN model files can be used via a component ANN model. The ANN model provides functions for accessing the trained device data.

• ANN training and testing.

  Let's assume we have a power amplifier device. From this device, we have measured 14 output characteristics as a function of three input characteristics: the real and imaginary parts of load impedance and the frequency. The output characteristics are shown in Table 1.

  To begin the training, the measurement data is sorted into two different files: a training file and a test file. For the ANN model generator, a number of layers and neurons in each layer have to be chosen. Finding the optimum value for layers and neurons can be an iterative process. After several simulation rounds, a satisfying result is achieved with five layers consisting of 3, 8, 12, 16 and 14 neurons respectively. The training took three minutes and 24 seconds using 50000 optimization cycles. Resulting training error was 1.105% and test error was 13.469%. The results could still be improved with more samples in the measurement data or with better layer-neuron combination. After the training, we have access to all 14 output values as a function of any input value combination provided that the input values are within the minimum and maximum values of the training set.

  Table 1. Output characteristics that are used by the ANN training.

  Table 1.
  Variable
  Pin
  Pout
  Gain
  Ids
  Dc power
  Collector dc power efficiency
  EVM (rms)
  EVM (max rms)
  EVM (av. peak)
  MS @ 400 kHz up (EDGE modulation spectrum at -400 kHz from carrier)
  MS 400 kHz up (EDGE modulation spectrum at +400 kHz from carrier)
  MS @ 600 kHz lo MS @ 600 kHz up
  95th percentile EVM

• Checking the ANN performance.

  The ANN performance is verified against reference interpolation functions. The reference interpolation data is obtained in the following way. For each test point, three closest measurement points are found (closest in the Smith chart). If the triangle defined by these points encloses the test point, a linear interpolation in the triangle is used. If the test point falls outside this triangle, a certain measure is used to determine if the test point is “far outside” or “not-so-far outside.” If it is “not-so-far outside,” the value is linearly extrapolated. If it is “far outside,” a set of next-closest measurement points is found, and a number of triangles are considered defined by these points. If the test point falls within these triangles, an average of the respective linear interpolations is used. If it is still outside all these triangles, the linear extrapolation of the first triangle is used (as in the case “not-so-far outside.”)

  Due to the inherent uncertainty in the measurement data and the “blind” nature of linear interpolation, the result necessarily contains some discontinuities. The more severe discontinuities result from the inability to perform meaningful extrapolation, as the measurement points do not always properly encircle the test point. In addition, the aforementioned interpolation method is complex to write and use. This is where ANN is most useful. In Figures 2 and 3, the gain and used direct current (dc) power of the measured power amplifier are shown as a function of the reflection coefficient angle theta. Each theta corresponds to selected test output impedance forming a spiral near the center of the Smith chart, as shown in Figure 4. In Figures 2 and 3, the curves shown in blue are the results of the reference interpolation functions and the curves shown in red and markers are the results of the ANN model.

  As can be seen from Figure 3, ANN gives more reliable results. Please note how ANN “smooths” the discontinuities.

Let's consider a case where we want to design a matching network for the power amplifier with requirements that the gain of the amplifier is more than 19 dB while the dc power used is less than 110 W. We have the measurement data of the amplifier: gain and dc power as a function of output impedance. After the ANN training, the ANN model contains these figures for any output impedance (in the measurement range) by means of interpolation. Now APLAC's optimization can be used in order to find the matching circuit component values so that our goals will be achieved. The ANN model can be used in setting the optimization goals. The procedure is as follows:

1. One-port (termination impedance 50 Ω) is used for measuring the impedance of the matching network.

2. This impedance is fed to the ANN model and the corresponding gain and dc power are read from the model.

3. The gain and dc power read from the ANN model are used in the goal definitions for the optimization.

The used LC-matching circuit is shown in Figure 5. Using APLAC's automated optimization methods, we were able to choose the component values so that the specifications were met. The results are as followed:

Figure 6 shows the output impedance of the power amplifier (the impedance to be matched) that resulted in the desired gain and dc power on Smith chart. The impedance was 0.049-36.345j Ω.

ANN models can also be used in statistical analysis (Monte Carlo). In this final step, the matching circuit components have been given statistical deviations (uniform distribution of 5% from nominal value) and a Monte Carlo simulation is run. In this example, the simulation has been repeated 5000 times. As a result, the distribution of dc power vs. gain along with the optimization limits can be observed as shown in Figure 7. From the distribution we can get a picture of different possible power-gain combinations. For more detailed information, a histogram of different dc powers can be viewed. The dc power distribution is shown in Figure 8. In the example case, 93.3% yield was achieved.

With artificial neural networking, we could easily and accurately interpolate measured multidimensional data and use the created ANN model in electronics design tasks. It was seen that the ANN model provided more reliable interpolation than ordinary numerical interpolation and the usage is much less complex. The approach can easily be expanded into any number and any kind of input and output data that is available. In order to use the approach for another device all you need to do is to measure the device and use the ANN model generator to generate the new ANN model.

1. APLAC RF Design Tool 8.10 reference manual vol. 1, Programming, Analysis and Optimization, April 2005.

Jarno Kyhälä received his MSc degree in electrical engineering from the Helsinki University of Technology, Espoo, Finland, in 2005. He has been working at APLAC Solutions Corp. (now AWR-APLAC Corp.) since 2002, where he is responsible for APLAC training and support as customer service manager. His main areas of interest include RF circuit design and simulation.

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