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. Subharmonic Mixer configured as a 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. There are currently discussions surrounding 6G and the 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.

To understand the properties that the subharmonic 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 the requisite combination of bandpass (BPF) and Low-pass filters (LPF) for subharmonic mixing.

Figure 2. Downconverter SHM using a 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, V_LO will be greater in magnitude than V_RF and is said to “pump” or “drive” the diodes.

V=V_LOsin(ω_LOt) + V_RFsin(ω_RFt)                                                             Eq. 2

The single diode I-V characteristic is shown in Figure 3b. As the applied V_LO 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.

Figure 3. Single Diode Mixer a) Circuit b) I-V curve c) Conductance curves

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

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 the signal to propagate out of the LO port and increase conversion loss. An example of this undesirable mixing response is shown in Figure 4; the yellow mixing product can escape out of the LO port.

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 applied voltage as indicated by Figure 5b.

Figure 5. Anti-Parallel Pair a) circuit b) I-V Curve c) Conductance curves

Now, irrespective of the applied voltage polarity one of the two diodes will be forward-biased and conducting. When looking 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, I_C, 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 the relationship mf_LO±nf_s  where m+n=even integer. These constitute the DC component, fundamental/odd harmonic mixing products, and even harmonics of the LO. The suppression 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.

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 suppressing 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.

mmWave Subharmonic 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. 

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

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 so the propagation of the fundamental mode is fully supported. Figure 8c shows the S21 simulation of a WR-12 waveguide with the cut-off frequency indicated by marker 1.

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 2f_LO suppression.

Why not use a harmonic mixer?    

If one of the main benefits of a subharmonic mixer is the ability to utilize 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 obvious 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 an SHM will necessitate 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.

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

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, is overlaid on a spectral plot shown in Figure 10a and 10b respectively.

Figure 10. Spectrum with filtering requirements WR-12 mixers a) Subharmonic 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 subharmonic 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 spectral 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 these signals would be difficult to identify and would likely prove problematic to filter out.

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 subharmonic 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 subharmonic widely applicable to many areas be that scientific, test and measurement, radar, or communication systems.