A quadrature mixer consists of two balanced mixers where the RF (or LO) ports are connected along with an in-phase power divider; the LO (or RF) ports are connected with a quadrature hybrid. There are two IF ports, “I” for the in-phase component and “Q” for the 90° out-of-phase component. They are available to the user for further signal processing (Fig. 1). Quadrature mixers can simultaneously mix ‘in-phase’ and ‘quadrature’ components. It leads to a variety of unique features and applications of these mixers. Phase detectors and single sideband modulators are two of these important applications.
Using a Quadrature Mixer as a Phase Detector
A phase detector is a device that generates a voltage signal which represents the difference in phase between two signal inputs. It is an essential element of the phase-locked loop (PLL). Detecting phase difference is very important in many applications, such as motor control, radar and telecommunication systems, servo mechanisms, and demodulators.
Theoretically, any mixer with a DC coupled IF port could be used as a phase detector. While it is true that even a single diode can be used as a mixer, most phase detectors involve the use of balanced mixers which offer high isolation between all three ports: the reference (LO), input signal (RF) and output (IF). Furthermore, the balanced mixers provide very low DC offset or residual voltage at the IF output.
The basic concept upon which phase detection rests is that with the application of two identical frequencies, constant amplitude signals to a mixer results in a DC output which is proportional to the phase difference between the two signals. The output at the IF port contains the sum and difference of the frequencies of the signal’s input to the LO and RF ports. If the input signal (RF) and the reference (LO) signals have identical frequencies, then their difference is zero Hz, or DC, which is the desired output for a phase detector. Their sum, which is twice the input frequency, can be selectively filtered out if it is not already beyond the frequency response of the IF port.
When the two signals are in phase with each other the voltage will be at a positive maximum, at 180° out of phase the voltage will be at a negative maximum, and when they are either 90° or 270° phased to each other the output will be purely imaginary, and the voltage will be (ideally) zero.
However, the above phase detector has its limitations: it is limited to a phase difference of ±90° and requires constant/stable signal amplitude. The good news is that this can be greatly improved by using a quadrature mixer as a phase detector.
The quadrature phase detector is used to mix the signal with two references, with the second reference being 90° with the first. This allows it to detect a phase difference of ±180°, which covers a full 360°.
Also, since I and Q are in quadrature, it is easy to calculate the phase between the two signals as
The calculated phase is almost linear with input phase after the correction factors. This is a significant improvement over the double balanced mixer, since we don’t need to know the input power levels and there is never any phase ambiguity, thus obviously very little variation in calculated phase with power.
Using a Quadrature Mixer as a Single Sideband Modulator
Any mixer will always produce both the sum and difference product, but in most cases only one of these products is desired. For this reason, the output signal of the mixer is usually filtered in order to reject the undesired product before the signal can be used. However, the quadrature mixer, also called: single sideband (SSB) mixer, image-reject mixer, and I/Q mixer, is a special type of mixer which is capable of attenuating the undesired product. The term “image” is conventionally used to describe the sum or difference product which is undesired from mixing.
This type of mixer forms the basis for the quadrature, or I/Q modulator. The quadrature modulator, which is able to perform single side-band frequency modulation, has the function of placing information on the carrier at the selected side band. Because of its simplicity and ease of use, quadrature modulators have been in wide use for decades.
It can be seen from Fig. 3 that the Single Side-band (SSB) modulator is actually two mixers with some quadrature phase shifting on the L and I ports of one of the mixers. With an ideal SSB modulator, the undesired products from each internal mixer arrive at the summing process exactly equal in amplitude and 180⁰ out of phase and thus are completely cancelled.
In the real world, if one wants to modulate an IF signal on an LO carrier at either the upper or lower sideband, he or she just needs to feed the IF into a quadrature modulator through a 90⁰ hybrid (operating at IF frequency), as shown Fig. 4.
By swapping the I/Q signals into the modulator, one can change Upper Side Band (USB) to Low Side Band (LSB) modulation, or vice versa.