# Digital or Analog? How Should I and Q Combining and Separation Be Done?

February 22, 2021 by Wes Brodsky## How should I and Q combining be done? Through analog or digital means? This article will discuss the basics of the analog and digital IQ approaches.

Analog IQ Modulators (for transmitters) and IQ Demodulators (for receivers) have been used for decades ([1] to [3]).

the Recently, new A/D and D/A Converters have been introduced, which can directly sample an IF at from 1 to 4 GHz; sampling in the 2nd, 3rd, and 4th Nyquist zones ([4] to [7]). These, combined with higher speed digital logic, allow the combining (for A/D) and separation (for D/A) do be done digitally ([8] to [21]). This is illustrated in Figure 1(a) (for a modulator) and Figure 1(b) (for a demodulator) with the Data Converter (DAC or ADC) in position “D”.

**Figure 1(a).** Modulator

**Figure 1(a).**Modulator

**Figure 1(b).** Demodulator

**Figure 1(b).**Demodulator

On the other hand, integrated analog I, Q combiners and separators have very good matching between the I and Q paths, solving some of the objections to doing these processes analogly. The analog technique also requires twice the data converters (A/Ds or D/As) than direct sampling at IF, but they run at lower sampling rates; so they are cheaper and require less power. This is illustrated in Figure 1(a) (for a modulator) and Figure 1(b) (for a demodulator) with the Data Converter (DAC or ADC) in position “A”.

The author starting thinking about this question. He asked for opinions on several LinkedIn groups, and received valuable answers. With the approval of the acknowledgees, they are acknowledged below. He also found out whatever information he could on the properties of contemporary Integrated Circuits (ICs) for these functions, and the results of whatever performance requirements had been determined for these ICs. From this, he tried to generate whatever general conclusions could be drawn to answer the question; “Should IQ Modulation and Demodulation be done Analogly or Digitally?”

### Analog IQ Approach

The analog IQ approach has been around for decades ([1] to [3]). Any IF or RF signal can be represented by

R(t) = I(t)cos(2πft) +Q(t)sin(2πft)

where f is the carrier frequency, I(t) is called the In-Phase component, and Q(t) is called the Quadrature component. An analog IQ modulator takes the baseband signals I(t) and Q(t) and forms R(t). This is shown in Figure 1(a) with the DACs in position A. An analog IQ demodulator takes as input R(t), and forms I(t) and Q(t). This is shown in Figure 1(b) with the DACs in position A.

A critical problem with the analog approach is maintaining the gains through the two paths to be identical, and the phase difference to be exactly 90º. Sometimes neglected for these requirements are the two Low Pass Filters. They should be exactly gain and phase-matched for all frequencies where there is significant signal energy. More exact quantification of these requirements, and the impairments caused by deviations from them, are shown in a later article.

### Digital IQ Approach

Recent developments in high-speed data converters (DACs and ADCs), have lead people to avoid the IQ imbalance problem discussed in the Analog IQ Approach section by implementing the IQ Modulator and Demodulator functions digitally, where the gain and phase can be produced with no error ([5], [8] to [21]). For the modulator case, there is a high-speed DAC at the output, as shown in Figure 1(a) with the DAC in position D. For the demodulator case, there is a high-speed ADC at the input, as shown in Figure 1(b) with the ADC in position B.

Often these digital approaches take advantage of the aliasing effect, using what is called bandpass sampling ([22] to [24]. [24A], [24B]). Figure 2(a) shows a waveform sampled in time. Figure 2(b) shows the spectra of the unsampled and sampled signal. The sample clock of the ADC is performing the same function as the Local Oscillator in an RF mixer. For an ADC, an analog filter can allow only a signal in one Nyquist zone to pass, and this mixing action can be used to downconvert a signal in that Nyquist zone to baseband.

**Figure 2(a). **Sampling in Time Domain

**Figure 2(a).**Sampling in Time Domain

*Figure 2(b). **The **spectra of the unsampled and sampled signal*

*Figure 2(b).*

For DACs, the output can be shaped in time to improve the performance at higher frequencies.

Figure 3(a) shows a “Normal” or “Non-Return to Zero” (NRZ) DAC output. After each sample, the output remains constant until the next sample. The analog spectrum is shown in Figure 3(b).

**Figure 3(a). **Sampling in Time Domain

**Figure 3(a).**Sampling in Time Domain

*Figure 3(b).*

*Figure 3(b).*

Figure 4(a) shows a “Return to Zero” (RZ) DAC output. After each sample, the output remains constant for half a sample period, and then goes to zero. This has the effect of increasing the amplitude in the second Nyquist zone, as shown in Figure 4(b).

**Figure 4(a). **Sampling in Time Domain

**Figure 4(a).**Sampling in Time Domain

*Figure 4(b).*

*Figure 4(b).*

Figure 5(a) shows a “Mix” or “RF” DAC output. After each sample, the output remains constant for half a sample period, and then goes to negative that value. This is same operation as a mixer which uses both polarities of the Local Oscillator waveform. The analog spectrum, shown in Figure 5(b), has an even larger amplitude in the second Nyquist zone. After a waveform is created via any of the above methods, the desired frequencies must be filtered out with a Low-Pass or Band-Pass filter, to remove whatever undesired alias and spurious responses there might be.

**Figure 5(a). **Sampling in Time Domain

**Figure 5(a).**Sampling in Time Domain

*Figure 5(b).*

*Figure 5(b).*

The digital approach avoids any problems with quadrature imbalance. However, all data converters have their own undesired impartments, due to quantization and sampling effects. Some of these effects will be shown in the next article. The cost and power requirements of these high-speed data converters are also often high, compared to analog IQ networks.

#### Acknowledgments

When the questions addressed in this report first appeared in the author’s mind, he solicited comments through some LinkedIn groups. Several useful responses were received. Those who gave permission for their personal information to be used are; Gary Kaatz, Khaled Sayed (Consultix-Egypt), Dieter Joos (ON Semiconductor), and Jaideep Bose (Asmaitha Wireless Technologies). The author also thanks his wife, Elizabeth, who probably wondered what her husband was up to; secluded in his home office, doing work he was apparently not being paid to do.

#### References

The following references will be used for each of the articles in this series.

Analog IQ Modulators and Demodulators: General Descriptions

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[2] Eamon Nash; "Correcting Imperfections in IQ Modulators to Improve RF Signal Fidelity "; Analog Devices Application Note AN-1039; 2009

[3] Anon; "An IQ Demodulator-Based IF-to-Baseband Receiver with IF and Baseband Variable Gain and Programmable Baseband Filtering "; Analog Devices Circuit Note CN-0320; 2013

High Speed Data Converters (DACs and ADCs); General Information

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[7] Alex Arrants, Brad Brannon and Rob Reeder; "Understanding High Speed ADC Testing and Evaluation"; Analog Devices Application Note AN-835, 2010.

Digital IQ Modulators and Demodulators

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Bandpass sampling (Rev .04 changed “subharmonic sampling” to “bandpass sampling)

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Effects of IQ Imbalance, no compensation or exploitation proposed

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7.6 Effects of IQ Imbalance, compensation or exploitation proposed

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7.7 Requirements for BaseBand DACs and ADCs

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Requirements for RF DACS and ADCs; and for RF Non-linearities

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7.9 Carrier aggregation for LTE-advanced; Wideband spectral requirements.

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