Plasma Diagnostics Diode Mixer Array
1. ECE Imaging Array System
A 2-D ECE imaging system has been well developed and applied on Tokamak Devices such as KSTAR, TEXTOR, etc. by UC Davis Plasma Diagnostics Group. A schematic of the 2-D ECE imaging system is shown below:
Figure 1.1 Complete schematic of the ECE Imaging system [source: C.W. Domier]
ECE radiation from the hot plasma is collected by the optical lenses. Before it is received by the array, a planar quasi-optical notch filter is used to protect the array against strong radiation from the Electron Cyclotron Resonance Heating. Since it is necessary to perform the down conversion process in single sideband, the dichroic plate, a metal plate filled with circular holes, acting as a high pass filter is employed, to suppress the lower sideband and allow the high frequency radiation to pass through with low loss. The RF signal received by the antenna array is then mixed with a local oscillator signal and down converted to a lower IF frequency and amplified by low noise amplifiers. The IF signal is then divided into 8 discrete frequency bands by the electronic circuits, with each band corresponding to a different horizontal position in the plasma, and down converted again by the local oscillator signal provided by VCOs on the RF board. Then the signals go to the IF board which consists of IF amplifiers, low pass filters, detectors, video frequency amplifiers and high speed digitizers which are used to sample the signals.
2. Diode Mixer
A planar antenna is a very attractive solution for our quasi-optical imaging receiver application. The desired antenna should have compact size, length less than one free space wavelength for high spatial resolution in the vertical direction, wide RF bandwidth (above 20%) for wide plasma coverage in the horizontal direction, high directivity (3dB beam width less than 20 degrees) for increased receiver sensitivity, low side-lobe levels (less than 10dB) to reduce inter-channel crosstalk, and linear polarization for receiving signal emitted from plasma modes of interest.
In order to down convert the ECE signal received by the planar antennas, we make use of the nonlinearity of diodes.
Figure 2.1 I-V characteristics of a Schottky Diode
The I-V relationship can be expressed as: .
Let the diode voltage be: , where V0 is the DC bias voltage and v is a small AC signal voltage. Then we expand the I-V relationship in a Taylor series about V0 as follows:[i]
The first derivative can be evaluated as:
The Second derivative can be evaluated as:
So we have:
Then, we have LO input signal , RF input signal , then we have the v2 term giving us the following output current:
For our down converting process, the term will become the IF signal. Other terms will be filtered by the following components such as IF balun and amplifier.
Figure 2.2 ECEI receiving end
Dual dipole antenna is chosen as the receiving antenna in current ECEI systems due to its wide frequency band, high directivity and low side band. Here is an example of a dual dipole antenna:[ii]
Figure 3.1 Dual dipole antenna
Since RF and LO frequency is close to each other, a single dual dipole antenna will receive both RF and LO signal. A diode is mounted in the middle of the dual dipole antenna mixing both RF and LO signals to down convert RF to IF (2-26.5 GHz).
This antenna has a very good pattern under mini-lenses (see Part 4) from 100-140 GHz. The measurement result is shown below:
Figure 3.2 Measurement result of the dual dipole antenna
4. Mini-lenses array
For printed circuit board antennas, the radiated power is concentrated in the higher dielectric constant region and would be trapped in substrate modes [iii], which is shown below:
Figure 4.1 Illustration of substrate mode
In order to take advantage of the radiated power and prevent it from being trapped in substrate modes, a dielectric lens must be used.
4.2.Front side LO coupling
A spherically, elliptically, or hyper-hemispherically shaped HDPE lens with dielectric constant of roughly 1.52 may be abutted to the substrate side of the printed lens array. It is shown in Figure 4.2 (a). This lens did an excellent job of collimating radiation from central elements; however it had the undesirable effect of imparting significant aberration on edge channels which are off the center of the lenses. Because of the limited amounts of LO power available, antennas resonant with the air side LO are employed rather than the substrate side RF. The antenna geometry is then fine-tuned to provide “clean” RF antenna patterns over the range of frequencies for which the LO power could be efficiently coupled to the array. In the other words, there is a compromise which needs to be made between optimizing the antennas for operation at the substrate and free space wavelengths. We chose to optimize the air side due to the lack of LO power.
In the current ECEI systems, a mini lens dual dipole antenna2 has replaced the former hyper hemispherical lens dual dipole antenna. Pictures for the mini lenses and antennas are shown in Figure 4.2 (b). Taking advantages of the excellent optical properties[iv], there is no need to consider the difficulty of feeding LO to the off-axis elements, since every element is positioned in the center of each mini lens in this configuration. With that freedom to feed both LO and RF from the front side, there is a much more careful optimization of the dimensions of the dual dipole antenna. The new dual dipole antenna shown in Figure 4.2 (b) is smaller than the previous one since we optimized it on the substrate side. As a consequence, the antenna pattern is much better.
Figure 4.2 Pictures for the former hemispherical dual dipole antenna and the miniature elliptical substrate lenses dual dipole antenna
X. Kong, et al. have shown the antenna measurement result and compared that with the previous oversized antennas 2.
(a) Test result with Mini-lenses
(b) Test result with big hemisphere lenses
Figure 4.3 Measured E- (left) and H-plane (right) pattern
4.3.Coupling of RF and LO
In order to couple RF and LO signal together, we make use of the beamsplitter.
Figure 4.4 Coupling of RF and LO using
By using a 3-dB beamsplitter, RF and LO are coupled together and each half of them is received by the mini-lenses array.
A mini-lenses array is fabricated for TEXTOR ECEI system2:
Figure 4.5 The mini-lenses array of the TEXTOR ECEI system
A total of 16 miniature elliptical substrate lenses of 15 mm diameter are arranged in a vertical array measuring 205.74 mm in height (center to center). Horizontal staggering of 11.684 mm (center to center) allows for reduced channel spacing in the E-plane, but results in a small offset in the H-plane between even and odd channels at the image.
5. Subharmonic Mixer
5.1.LO difficulty at high frequency
At high frequency, the lack of LO power becomes the most important issue for millimeter imaging applications. For fundamental mixing, LO frequency is close to RF frequency. When RF frequency is high, LO source is either difficult or expensive to get. So we need to consider other method of down converting.
Figure 5.1 Fundamental and subharmonic mixer
Subharmonic mixer, which is different with the fundamental mixer, requires only a LO frequency half of the RF frequency. Therefore, LO source will be much easier to get at higher RF frequency.
5.2.Subharmonic mixer principle
Similar to fundamental mixer, we still make use of the non-linearity of diodes, howeve, we use an anti-parallel diode pair here. There is considerable literature introducing the basic theory about subharmonic mixers[v][vi][vii]. A typical diode pair is shown in Fig. 5.2.
Figure 5.2 Anti-parallel diode pair mixer
Using the same way we dealing with fundamental mixer, we can derive the output current as:
The output current implies that the total output current will contain (2ωLωs), (4ωLωs)… harmonics. That means, this anti-parallel structure can suppress the odd-order harmonics of the LO (or suppress the even order inter-modulation terms) and realize second-order, fourth-order subharmonic mixing.
The odd-order harmonic suppression feature can also be illustrated by the I-V curves of the anti-parallel diode pair.
Figure 5.3 I-V curve comparison of single and anti-parallel diode pair
It is very clear for a sinusoid wave guiding through the diode and diode pair:
(a) Single diode waveform
(b) Anti-parallel diode pair waveform
Figure 5.4 Current waveform of a sinusoid wave
Ø Separate RF and LO antennas
Figure 5.5 Schematic of the subharmonic mixers with separated antennas
Back to back diodes will be pumped by the LO at half the RF frequency. The diode pair will be evaluated both at RF and LO frequencies and impedance matching will be done at both frequencies with the antennas. An LO short (λ/4 @ LO stub) is placed after the RF impedance match network to make sure all the LO power is transferred to the diode pair. Like the RF port, the LO impedance matching network is necessary to match the diode with the LO port. In addition, an RF short (λ/2 @ RF short stub) should be placed after the diode pair to short the RF. Also, these short stubs provide IF and DC paths to the ground. The RF and LO signals will mix at the diode pair and the mixed IF signal will be transmitted through the RF port and the undesired components will be filtered by the IF filter. Slot dual dipole antennas are used here.
Ø Single antenna for both RF and LO receiving
Wide band antenna such as log-periodic antennas may be utilized here to receive both RF and LO antenna at the same and then mix them at the anti-parallel diode pair.
Figure 5.6 Single antenna schematic which is similar to previous fundamental mixer
Log-Periodic antenna can be used for its wide band characteristics. It has been already widely studied and used in millimeter wave applications.[viii]