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What is a Sub Harmonic Mixer?

 

Sub Harmonic mixers (SHM) can be considered a sub-set of the Harmonic mixer category. They are designed to work using the second harmonic of the applied local oscillator (LO) to mix with the radio frequency (RF) signal to create an intermediate frequency (IF). The mixing relationship is governed by Equation 1.

 

IF=RF±(2×LO)                                                                      Eq.1

 

Figure 1 sub harmonic mixer configured as downconverter

Figure 1 Sub harmonic Mixer configured as downconverter

 

This type of mixer is commonly used in the millimeter wave region for applications such as radiometric sensors/receivers for ground-based astronomy, atmospheric sensing and imaging/radar systems [1-3]. There are currently discussions surrounding 6G and use of wide bandwidth communication systems in the sub-THz spectrum and the sub harmonic mixer has the potential to be a key enabler of this technology [4-7].

 

To understand the properties that the sub harmonic mixer offers it is beneficial to look at the basic diode configurations.

 

Single-Diode Struggles

 

Figure 2 shows the simple single Schottky diode configuration and requisite combination of bandpass (BPF) and Low-pass filters (LPF) for sub harmonic mixing.

 

 

Figure 2 downconverter shm using single diode

Figure 2 Downconverter SHM using single diode

 

In the downconverter configuration the RF and LO signal are applied to the mixer. Figure 3a shows the voltage across the diode which is given by Equation 2. Of these two voltages applied to the diode, VLO will be greater in magnitude than VRF and is said to “pump” or “drive” the diodes.

 

V=VLOsin(ωLOt) + VRFsin(ωRFt)                                                   Eq. 2

 

The single diode I-V characteristic is shown in Figure 3b. As the applied VLO voltage pumps the diode it drives it into forward conduction and the diode turns on. Similarly, when the applied voltage goes negative, the diode turns off.  This relationship between the applied LO voltage and the diode’s I-V curve is given by the conductance in Figure 3c.

 

Single diode mixer a) circuit b) i-v curve c) conductance curves. Adapted from [8]

Figure 3 Single Diode Mixer a) Circuit b) I-V curve c) Conductance curves. Adapted From [8]

 

When a single diode is driven in this manner the output current, I,  contains all combinations of mixing products mfLO±nfRF where m & n are integer values [8]. This indicates the single diode will work as subharmonic mixer as the 2fLO±1fRF mixing term is present. However, it is also more likely that the fundamental frequency mixing response, 1fLO±1fRF, will be more influential than that of the second harmonic and subsequently cause inteference at the IF [9].

 

A secondary concern of the single diode mixer is certain RF signal mixing products could appear within the LO BPF passband response. This will allow signal to propagate out of the LO port and increases conversion loss. An example of this undesirable mixing response is shown in Figure 4; the yellow mixing product are able to escape out the LO port.

 

 

Single diode fundamental interferers

Figure 4 Single Diode Fundamental Interferers

 

Double the diodes…halve the harmonics?

 

To improve upon the single diode mixer the well-known anti-parallel pair is exploited, this is given in Figure 5a. This topology presents a symmetric I-V curve to the to the applied voltage as indicated by Figure 5b.

 

Anti-parallel pair a) circuit b) i-v curve c) conductance curves. Adapted from [8]

Figure 5 Anti-Parallel Pair a) circuit b) I-V Curve c) Conductance curves. Adapted from [8]

 

Now, irrespective of the applied voltage polarity one of the two diodes will be forward biased and conducting. When lookin at the total combined conductance of the two diodes given in Figure 5c, it is easy to see how a second harmonic response is produced from the LO.

 

This diode configuration leads to the generation of a circulating current, IC, as indicated in Figure 5a. This circulating current is generated by the individual currents from each diode, I1 and I2. These currents have certain harmonic and frequency mixing components that are opposite in phase and will cancel when combined to generate the external current, I. These frequency components that cancel out externally are governed by relationship mfLO±nfs  where m+n=even integer. These constitute the DC component, fundamental/odd harmonic mixing products and even harmonics of the LO [8]. The supression property of the anti-parallel pair is predicated on there being a good electrical property match between the diodes.

 

As these frequency components cancel out they will be attenuated externally to the anti-parallel pair and will therefore be minimized at the outputs of the mixer. A representative example of this is shown in Figure 6; the red components indicate a signal that will be attenuated whereas the black components are not.

 

Spectrum showing suppressed and unsuppressed mixing products from shm

Figure 6 Spectrum showing suppressed and unsuppressed mixing products from SHM

 

The anti-parallel pair is therefore able to improve conversion loss of subharmonic mixing by supressessing the fundamental mixing products whilst also reducing filtering requirements at the output. This anti-parallel pair improvement brings the conversion loss of a well designed sub-harmonic mixer to a comparable value provided by fundamental mixers. There are other benefits to this topology as it can also lower the LO AM noise as well as provide protection against large peak voltages. [8,10]

 

mmWave Sub harmonic Mixers

 

The subharmonic mixer uses an applied LO of half the RF frequency and while this is applicable at any frequency this becomes particularly useful in the mm- and sub-THz bands; where generating an LO for a fundamental mixer is challenging.

 

Sub harmonic mixers at mmWave frequencies will commonly utilise waveguides as they have superior performance for insertion loss over microstrip. Figure 7a and 7b show a sub harmonic mixer with a WR-12 waveguide at the RF port covering 60-90GHz and an WR-22  waveguide covering 30-45GHz for the LO port, the IF port is typically and SMA or K-type connector.

 

Wr-12 sub harmonic mixer a) block diagram b) physical unit with waveguide ports

Figure 7 WR-12 sub harmonic mixer a) Block diagram b) Physical unit with waveguide ports

 

Using a waveguide to interface to the diodes is beneficial not only from an insertion loss perspective but as they also have a lower frequency cut-off, the fundamental or TE10 mode is not supported thus making them a low-pass filter. Figure 8a shows the E-fields at 30GHz in a WR-12 waveguide and it is clear that it is not able to propagate. Whereas Figure 8b has an E-field plot at 60GHz which is above the cut-off and so the propagation of the fundamental mode is fully supported. Figure 8c shows S21 simulation of a WR-12 waveguide with the cut off frequency indicated by marker 1.

 

Hfss simulation wr-12 waveguide a) e-field at 30ghz b) e-field at 60ghz c) plot of insertion loss

       Figure 8 HFSS Simulation WR-12 Waveguide a) E-Field at 30GHz b) E-Field at 60GHz c) Plot of insertion loss

 

The highest frequency LO signal that can be applied to the WR-22 LO port for correct operation of the WR-12 SHM is 45GHz. This is still well below the cut off frequency of the WR-12 RF port and when looking at marker 2 in Fig 8C it is clear it will be attenuated.

It is this natural waveguide cut-off frequency as well as the diode anti-parallel configuration that gives the SHM at mmWave frequencies its inherent LO-RF rejection along with the 2fLO supression.

 

Why not use a harmonic mixer?

If one of the main benefits of a subharmonic mixer is the ability to utilise a LO at half the RF signal then logically a harmonic mixer has increased benefits as it works off a higher harmonic. This further reduces design requirements for LO frequency generation.

 

The first and most obivous drawback of this approach is that working with a higher harmonic will cause an increase in conversion loss, thereby reducing the performance of the mixer.

 

Secondly, a higher harmonic for the same RF band as a SHM will neccessitate that the LO starts to go down in frequency. While this is desirable for the aforementioned LO generation, it will start to encroach into the available bandwidth for the IF. This can be a limiting factor for wideband applications such as communications in the mmWave and sub-THz regions where there is good availability of spectrum and allows for greater channel capacity [7].

 

To illustrate this point a harmonic mixer utilising the sixth harmonic of the LO, Figure 9a & 9b, with a WR-12 RF output can be compared to a similar WR-12 SHM.

 

Wr-12 harmonic mixer a) block diagram b) physical unit with in-built diplexer

Figure 9 WR-12 Harmonic Mixer a) Block diagram b) Physical Unit with in-built diplexer

 

A representation of the two required filter responses, for the sixth harmonic and SHM, are overlaid on a spectral plot in shown Figure 10a and 10b respectively.

 

Spectrum with filtering requirements wr-12 mixers a) sub harmonic mixer b) harmonic mixer

Figure 10 Spectrum with filtering requirements WR-12 mixers a) Sub harmonic mixer b) Harmonic mixer

 

Looking at the harmonic mixer in Figure 10b the LO filter is closely located to the IF, which as a diplexer shown in Figure 9a means they cannot overlap, this limits the available IF BW. Comparatively when looking at the sub harmonic mixer spectrum in Figure 10a the LO is operating in the 30-45GHz range which allows the IF BW to be extended much further.

 

By inspection of the two spectal responses shown in Figure 10 it becomes apparent that there is more risk of mixing products and spurious signals appearing in the RF band with a harmonic mixer. The source of this signals would be difficult to identify and would likely prove problematic to filter out.

 

Then a Fundamental Mixer?

 

The designer may now be thinking if the harmonic mixer has the worst conversion loss, spurious mixing products and IF BW, then a fundamental must be the way to go. The conversion loss of a subharmonic mixer is of comparable level to that of a fundamental mixer due to the anti-parallel pair configuration. The designer will have to generate an LO multiplier chain that goes up to RF frequencies to drive the mixer, which comes with its own challenges at the mmWave frequencies.

 

Summary

 

The sub harmonic mixer is a versatile device that helps the designer by reducing the LO frequency generation requirements by half while providing mixing product suppressions and maintaining a good conversion loss. It is these attributes that make the sub harmonic widely applicable to many areas be that scientific, test and measurement, radar or communication systems.

 

References

[1] R. Hu, Y. Chen, and K.-H. Hsieh, “Wide-IF-Band 90-nm CMOS Image-Rejection Subharmonic Radio-Astronomical Array Receiver Design in 75–110 GHz,” IEEE Transactions on Terahertz Science and Technology, vol. 12, no. 5, pp. 464–470, Sep. 2022, doi: https://doi.org/10.1109/tthz.2022.3181467.

 

‌ [2] Olivier Auriacombe, V. Vassilev, and N. Pinel, “Dual-Polarised Radiometer for Road Surface Characterisation,” Journal of Infrared, Millimeter, and Terahertz Waves, vol. 43, no. 1–2, pp. 108–124, Jan. 2022, doi: https://doi.org/10.1007/s10762-022-00847-5.

 

[3] R. Dahlback, T. Bryllert, G. Granstrom, Mattias Ferndahl, Vladimir Drakinskiy, and J. Stake, “Compact 340 GHz homodyne transceiver modules for FMWC imaging radar arrays,” Chalmers Research (Chalmers University of Technology), May 2016, doi: https://doi.org/10.1109/mwsym.2016.7540113.

 

[4] ZHANG B, WANG Y H, FENG Y N, et al. A 220 GHz frequency-division multiplexing wireless link with high data rate [J]. ZTE Communications, 2023, 21(3): 63–69. DOI: 10.12142/ZTECOM.202303009

 

[5] T. J. Chung, “10-Gbit/s Wireless Communication System at 300 GHz,” ETRI Journal, vol. 35, no. 3, pp. 386–396, Jun. 2013, doi: https://doi.org/10.4218/etrij.13.0112.0351.

 

[6] Y. HE, G. LIU, J. LIU, C. LIN, and W. SU, “A 220 GHz Orthogonal Modulator Based on Subharmonic Mixers Using Anti‐Paralleled Schottky Diodes,” Chinese Journal of Electronics, vol. 31, no. 3, pp. 562–568, May 2022, doi: https://doi.org/10.1049/cje.2021.00.270.

 

[7] J. Borrill, “What is behind the drive towards Terahertz technology of 6G”, Anritsu, 2021. [Online]. Available: https://apsr.anritsu.com/en-sg/tm/whatisbehind-drive6gtecnology

[8] M. Cohn, J. E. Degenford, B. A. Newman, ”Harmonic Mixing with an Antiparallel Diode Pair”, IEEE MTT-S Vol. 23, No. 8, pp. 667-673, August 1975.

 

[9] S.A. Maas, Microwave Mixers. 1986

 

[10] E. R. Carlson, M. V. Schneider, and T. F. McMaster, “Subharmonically Pumped Millimeter-Wave Mixers,” IEEE Transactions on Microwave Theory and Techniques, vol. 26, no. 10, pp. 706–715, Oct. 1978, doi: https://doi.org/10.1109/tmtt.1978.1129474.

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