Frequency Independent Phase Shifter

Precise Solution

Phase shifters are important to a variety of digital and analog communication applications. Traditional phase shifters are designed to operate only at a single frequency, requiring cumbersome techniques to maintain the phase for large range of frequency. In this article, Nishant presents an implementation of frequency independent phase shifter. It’s able to reduce the effect of frequency on phase and make a system independent of frequency in the range of 4kHz to 7kHz.

This article presents the implementation of a frequency independent phase shifter using basic building blocks of analog circuits, such as op amps, JFETs and passive devices. As mentioned earlier, traditional phase shifters are designed using an all pass filter, with a phase shift varying from 0 degrees to 180 degrees for a given frequency. A slight variation of frequency would lead to a drastic change in the phase. This varying phase may be a problematic issue in some critical communication related applications and would make the system highly frequency dependent. Here, we simplify the system to reduce the effect of frequency on phase and make a system independent of frequency in the range of 4kHz to 7kHz.

SOME BACKGROUND
Research has been done to make efficient phase shifters that are frequency independent. Some researchers have built them using programmable floating resistors. That design approach is based on a simple op amp phase shifter with a programmable floating resistor and a programmable capacitor. The phase shift can be varied using the programmable resistor. Compensation for the variation in the frequency is achieved using the programmable capacitor. Figure 1 shows the diagram of this implementation.

Another technique for crafting frequency independent phase shifters involves converting the input signal using a frequency-to-voltage converter (FVC) and using the resulting voltage to control the voltage control resistor (VCR). Here, the VCR is implemented using a JFET and a voltage-controlled oscillator (VCO). Figure 2 shows the block diagram of that circuit.

Those two designs that we’ve described so far are all costly techniques and require special function ICs for their operation. Moreover, they produce results that are not 100% accurate for the range of frequency defined. The same approach has been used to employ a variable resistor-based circuit to make the phase shifter frequency independent. It uses the JFET’s properties to act as variable resistor.

There’s a reason why all pass filters are a commonly used to build phase shifters. The characteristics of the all pass filter is such at its magnitude does not vary with frequency, but the phase shift does change with frequency. But the main drawback of such a circuit is that the circuit components must be chosen for a specific frequency. If we vary the frequency, the phase shift changes. So, to make the circuit frequency independent, we can vary a component of the all pass filter with the frequency of the input voltage. In this proposed scheme, I have replaced the resistor in the filter with a JFET that has a controlled gate voltage. By using proper feedback, the gate voltage of the JFET is varied such a way that its drain-source resistance is set to a proper value according to the input frequency and thus the required phase shift is achieved. Figure 3 shows a simple block diagram of this system.

For the feedback, first the phase output of the all pass filter is detected, which gives a DC output corresponding to the phase output. Now this voltage is compared with a reference voltage with the help of a differential amplifier. The output of the differential amplifier is fed back to the JFET gate voltage. So, if the phase output of the all pass filter is high, it will give a higher DC voltage. And the JFET gate feedback voltage will increase so that the resistance will decrease and the phase of the all pass filter will decrease to the desired value.

THE CIRCUIT DESIGN
Now, let’s examine each element and criteria of the circuit.

All pass filter: An all pass filter is a filter whose magnitude response is fixed but phase response varies with frequency. Figure 4 shows the circuit diagram of an all pass filter.

Control waveform generator: First, we generate two switching waveforms: one derived from the filter and another 180-degree phase shifted. We then send the input to a buffer. That’s because giving it directly to the comparator may cause loading to the input. The output of the buffer goes to the comparator and this output is then inverted with the help of an inverter.

Phase shift detector: First, we have a buffer from the all pass filter. A two-input multiplexer is built, essentially like a structure with four switches. One of the inputs to the multiplexer is the output of the buffer and another one is the inverted signal of this output. The control to the switches is done from the switching waveforms derived from the input pulse such that when the input is high, the output of the phase shifter will pass. When the input is negative, it’s inverted version will pass.

We then have a low pass filter which will average out the two signals. Here the switches are placed in a way such that they are seeing either ground or virtual ground so that the voltage across the switch is not changing. So, the ON resistance of the switches does not vary with the input voltage change. Furthermore, the switches are not dependent on the input voltage in this architecture. If we interchanged the series and parallel switch positions, the resulting circuit would have a problem whereby the offset voltage would be multiplied by a huge gain, causing the amplifier to saturate. With that in mind, we can conclude this is the optimal switching scheme for the multiplexer.

Now we need to design for various phase shifts. From Figure 5, you see that the output of the phase shift detector must be 0V for 90 degrees and other phases require different V_ref values. We now have a difference amplifier whose one input is the output of the phase detector and another one is ground as a reference of 0V for 90 degrees and finite values for other phases.

JFET can be used as a variable resistor. A VCR may be defined as a three-terminal variable resistor where the resistance value between two of the terminals is controlled by a voltage potential applied to the third. Figure 6 shows the complete circuit diagram.

COMPONENT SELECTION
Resistance values of standard 10kΩ were chosen for the all pass filter’s amplifier. The 0.1uF capacitor is connected toward the filter. Note that a ceramic capacitor could be used here instead of an electrolytic type because an electrolytic capacitor has less tolerance. JFET component BFW10 was chosen because its ON resistance is around 150Ω (typical). This design is for the frequency range of 4kHz-8kHz. From the theory, we know that, for a 90-degree phase shift, ωRC=1. So, capacitance (C)=0.1µF, frequency (f)=10kHz and the required resistance is 159Ω. With f=20kHz, the required resistance is 79Ω, which can be obtained from the chosen JFET. I selected the BFW10 over the BFW11 because the pinch off voltage of the BFW10 is -6V, while for the BFW11 it is -2V. BFW10 and BFW11 JFETs are available from several manufacturers.

In the phase detector section of the circuit, the resistance values are chosen to be 10kΩ each, except for the final stage where it is kept at 100kΩ. The switches used are Texas Instruments (TI) CD4016s. Here, we could also use the TI CD4066 in multiplexer operations. For the low pass filter capacitance, I chose 0.1µF. The value of that capacitor was chosen according to the minimum frequency that we want to reject. Here, the resistance is 100kΩ, so the RC time constant is 1/100 which enables us to reject all the frequencies almost to 20Hz.

In the control waveform generator section, I used 741 op amps as comparators. And after that I used the 74C04 as my CMOS inverter because it has the advantage of being CMOS compatible and can be operated with a power supply other than 5V. The power supply can be either designed into the system, or the system can be powered externally from a ±9V source.

OBSERVATIONS AND CONCLUSION
In my observations, I experimented with different frequencies and phases. The input voltage was varied from 500mV to 1V, and a 90-degree phase shift was obtained over the frequency range of 5kHz-8kHz. In Figure 7 all the readings have been captured. Here it is observed that V_dc varies linearly over the change in phase and V_ref. Also, the graph shows constant phase for 80, 90 and 100 degrees over a frequency range of 4kHz to 7kHz, with slight variations in beginning in the side bands.

As frequency is increased, to maintain the same phase shift the resistance value must decrease. From the JFET characteristics, we have seen that its resistance decreases if its gate voltage increases. In Figure 7 the same trend is observed if you give external voltage to the JFET and try to obtain the required phase shift with varying frequency. Figure 8 shows phase shifter operation on a screenshot from an oscilloscope.

Our precise frequency independent phase shifter was designed in the range of 4kHz-8kHz. A tolerance of 5 degrees for the frequency range of 4kHz-8kHz was obtained. For this this project, I relied on an accumulation of learning from various research papers, so it’s an adoption of an existing approach. The links for this article in RESOURCES below include some good research papers that will help you take this project further. The scope of this project could be extended by increasing the range of frequency over which the phase is constant.

That wider scope would need to explore more resistance and capacitance values. We can increase the linearity range of the phase shifter by having various capacitors of different values at different frequency ranges. By using a microcontroller (MCU), we could select the capacitor of our required frequency range so that—within that range—we will get the required degree phase shifted output. The MCU could also be used to control the reference voltage to increase the range. 

RESOURCES

Reference:
[1] https://iopscience.iop.org/article/10.1088/0022-3735/12/11/006/meta

https://www.researchgate.net/publication/4255446_Frequency_Independent_Phase_Shifter

FET as Voltage controlled Resistor AN105, Siliconix 1997

Variable frequency passive phase shifter, Flarity Warren H

Texas Instruments | www.ti.com

PUBLISHED IN CIRCUIT CELLAR MAGAZINE • SEPTEMBER 2020 #362 – Get a PDF of the issue

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