1. Introduction

Recently,the demand for low noise receivers at millimeter and submillimeter waves increased dramatically. These receivers are widely applied in various fields,such as space applications,meteorology and geosciences,mm-wave imaging and radio astronomy. Two detection techniques are adopted,named direct detection and heterodyne detection. Direct detection systems have the advantages of broad bandwidth,and the local oscillator is not needed. Therefore,the direct detection receiver is especially attractive in low cost passive millimeter wave imaging for large-scale production. One of the key components in the direct detection receiver is broadband high sensitivity and high linearity detectors. Sensitivity of detectors is expected as high as possible in order to reduce required gain of the low noise amplifier. A zero bias Schottky diode is adopted to simplify the detector design,eliminate the biasing circuitry and related noise,and reduce current induced modulation flicker and burst noise^{[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]}.

Recently,detectors with Sb-heterostructure diodes have high sensitivity,superior noise,and much lower dynamic junction resistance properties at zero bias. When properly matched,the Sb-diodes can produce sensitivity of more than 10000~mV/mW at W-band over broad bandwidth^{[1, 2, 3, 4]}. However,the Sb-diodes are not commercially available,so commercial GaAs zero bias Schottky diodes are used for detectors in this work. Currently,W-band commercial GaAs zero bias Schottky diodes are from VDI and ACST,the detector diodes from them can gain several times higher sensitivity than designs based on Aeroflex Metelics MZBD-9161 detector diode because of their low zero bias capacitance^[7]. However,the diode MZBD-9161 is low cost,so it is applied for in work. In order to predict the performance of the detector,a full-wave 3D-EM simulation of the diode is setup to investigate the optimum embedding impedances by replacing the active part of the diode with an internal coaxial port. The non-linear junction and passive circuit part are combined together in ADS for diode embedding impedances extraction. Once the diode embedding impedances are confirmed,subcircuits of the detector can be designed separately,and then the complete circuit of the detector is optimized. The $S$-parameters of the whole circuit are exported to Advanced Design System (ADS) for harmonic balance simulation with optimization goal of high sensitivity. For the W-band detector,the highest measured voltage sensitivity is 11800 mV/mW at 100 GHz,and the sensitivity is higher than 500 mV/mW in 75-110 GHz. Measured TSS is higher than -38 dBm. For the D-band detector,the highest measured sensitivity is 1600 mV/mW at 128 GHz,and the typical sensitivity is 600 mV/mW in 110-170 GHz. TSS is superior to -29~dBm. The linearity of the two detectors is superior to 0.9996.

2. Circuit design

The detector design flow chart is as follows. First,the $S$-parameters of the diode model in HFSS are exported and the diode optimum impedance is calculated. Second,the detector circuit is divided into three parts,which are input waveguide-microstrip transition,input matching circuit and output low pass filter. Each part is optimized,and the complete circuit is then setup in HFSS and its $S$-parameters are exported for detector sensitivity analysis.

2.1 Diode embedding impedances

Low barrier beam lead diode MZBD-9161 from Aeroflex is adopted in this work. The diode chip is designed for operation up to 110 GHz and no bias is required for high voltage sensitivity. The non-linear Schottky junction model is modeled by SPICE parameters,which are adopted in the diode model in ADS to characterize the diode nonlinear characteristics. The diode size is 0.7 $\times$ 0.25 mm$^{2}$,with $C_{\rm jo}$ $=$ 0.03 pF,$I_{\rm s}$ $=$ 1.2 $\times$ 10$^{-5}$ A,$R_{\rm s}$ $=$ 20 $\Omega$,and $n=$ 1.2. In order to accurately predict the diode chip optimum embedding impedances,a full-wave 3D EM simulation of the diode chip in its circuit environment is analyzed to find its optimum embedding impedances. An internal coaxial port is applied at the Schottky diode junction,and the diode non-linear part and passive circuit part are combined. The diode pad interface has been extruded and the transmission line ports are later de-embedded back to the diode reference planes,as described in Figure 1. It is an essential operation that enables precise modeling,actually if the ports are too close to discontinuities they can interfere with the near field around these discontinuities and therefore effect calculations. The $S$-parameters of the diode chip are exported for diode model embedding impedances discussion in ADS. The diode is connected to the internal port. With the harmonic balance simulator,the diode input impedance (Z-diode) is calculated. The values of the Z-diode will be used thereafter to synthesize the real detector. For the ideal detector,the optimum RF impedance of the detector is Z-RF $=$ (Z-diode)$^{\ast }$.

2.2 Circuit optimization

A typical schematic of a millimeter wave detector circuit is shown in Figure 2. While in this work,RF signals are coupled to a microstrip by antipodal finline transition^[14] and probe transition^[15],respectively,the finline transition does not require back short and eliminates the requirement for designing a complicated DC return path. The conventional application range of the finline circuit technology covers the frequencies in 10-110 GHz,and which gives the place to probe transition in the D-band detector. To increase the operation bandwidth,the detector circuit adopts additional matching elements in the input waveguides,together with a succession of waveguide sections with different heights and lengths.

Once the optimum RF embedding impedance ($Z_{\rm RF})$ is found,the matching circuit can be designed. The RF matching circuit is composed of high and low impedance lines for maximum transmission of the RF signal to diode. The input low pass filter (LPF) is also composed of high and low impedance lines,which provides a DC ground,and allows the diode junction capacitance to discharge. It also prevents the leakage of the RF signal and provides an open circuit. Transmission line L1 together with the output radial stubs LPF are designed to provide a broad band RF short for the detector diode and to isolate the RF signals. Usually,the RF chip capacitors are poor short circuits at W-band because of their low self-resonance frequency. Any quarter-wavelength type of structure is inherently narrowband. Nevertheless,microstrip filters with low impedance at first stage next to diode output tend to create a consistent RF short over a broadband width. Therefore,the width and length of line L1 are optimized for required reflection phase angle to create a short circuit to RF signals with maximum frequency bandwidth. The detector works in small signal condition,so the generated output harmonics of the RF signal are ignored to reduce the solving time.

When all subcircuits of the detector are optimized,the complete circuit is simulated. The multiport $S$-parameters of this simulation are extracted and then combined with a nonlinear detector diode to model the voltage sensitivity in the circuit simulator as shown in Figure 3. This process is repeated to optimize the detector sensitivity.

3. Experimental results

The substrate of the W-band detector circuit is RT/duroid5880 with dielectric constant of 2.22,and thickness of 0.127 mm. The D-band detector circuit substrate is ultra thin quartz substrates with dielectric constant of 3.78,and thickness of 0.08 mm. The substrates are mounted to the block with silver epoxy (type H20E from Epotek). The split block is manufactured by brass and electroplated with gold. The W-band and D-band detector photos are given in Figure 4.

The W-band and D-band detector measurement setup is presented in Figure 5. The input RF power of detectors is accurately controlled by Mi-Wave attenuator,and it can be precisely monitored by millimeter and submillimeter power meter PM-4. The detector output voltage is connected with OP27 operational amplifier with gain of 30 dB. Measured voltage sensitivity of the two W-band detector samples are depicted in Figure~6. The highest measured sensitivity is 11800 mV/mW at 100~GHz. The sensitivity is higher than 2000 mV/mW in 80-104 GHz,and better than 500 mV/mW in full W-band. Measured typical return loss is -5 dB as shown in Figure 7. Measured detector output voltage as a function of input power at 95 GHz is shown in Figure 8. The test data demonstrates good linearity,which is superior to 0.99992 at 95 GHz with power lower than -30 dBm. The response decreases as the input power is greater than -20 dBm,which corresponds to the transition region from square law to linear law detection response. The measured TSS is superior to -38 dBm as described in Table 1.

Measured voltage sensitivity of the D-band detectors with two different frequency bandwidths are depicted in Figure 9. The highest measured result is 1600 mV/mW at 128 GHz,and typical sensitivity is 600 mV/mW in 110-170 GHz. Table 2 shows TSS is superior to -29 dBm. Tested typical return loss is $-4$ dB as shown in Figure 10. Measured detector output voltage as a function of input power at 150 GHz is shown in Figure 11. The tested data also demonstrates very good linearity,which is superior to 0.99961 at 150 GHz with power lower than -10 dBm. The response decreases as the input power is greater than -10 dBm,which corresponds to the transition region from square law to linear law detection response.

Table 3 demonstrates commercial detector products' performance employing low barrier GaAs detector diodes. Obviously,the voltage sensitivity of the proposed detector is high and superior,and its sensitivity response has much wider frequency bandwidth. While comparing with recently reported detector papers with GaAs diodes,it can be concluded that the designed detectors reach their performance.

4. Conclusions

W-band and D-band detectors are analyzed and designed with low barrier Schottky diodes. Full-wave analysis and harmonic balance analysis are combined to find diode embedding impedances of the detector. The circuit input matching network is optimized by low and high impedance microstrip lines,and the output circuit is composed of an RF band stop filter and a tuning line for optimum reflection phase for RF signals. $S$-parameters of the complete circuit are used for voltage sensitivity analysis. For the W-band detector,the highest measured voltage sensitivity is 11800 mV/mW at 100 GHz. The sensitivity is higher than 2000 mV/mW in 80-104 GHz,and measured TSS is higher than -38 dBm. For the D-band detector,the highest measured voltage sensitivity is 1600 mV/mW,the typical sensitivity is 600 mV/mW in 110-170 GHz,and TSS is superior to -29 dBm. The detectors demonstrate very good linearity at millimeter wave band. The designed detectors are simple,low cost and compact,which is very attractive for test instruments,passive millimeter wave imaging and corresponding application systems.