### Introduction

When generating analog or digital FM for communications applications, an IQ modulator provides a versatile and low-power solution. An example design will show how a mixed-signal MCU is used to perform the phase accumulator and sine/cosine lookup table functions. The importance of IQ Modulator accuracy and linearity is demonstrated.

### Applications

FM is useful because of the high PA efficiency that is easily attainable. At the product level, applications can be wireless mics, headset and helmet radios, and handheld 2-way radios.

Some digital FM modulation schemes are Continuous-phase Frequency-shift keying (FSK), GFSK, and M-ary FSK. The DMR modulation standard, popular in the commercial 2-way radio business, utilizes narrow-band 4FSK which could be generated as described here. ^{1} Analog FM can be wide-band FM, or narrow-band FM (NBFM), as discussed below.

### Why use an IQ Modulator?

Many classic circuit techniques exist for generating FM, for example adding modulation into a PLL either at the VCO or the reference oscillator, or both. Reactance modulation is another classic method. The downside to these approaches is that the design becomes specific to a frequency band and the individual PLL or reactance modulator for that band. For example, variations in K_{vco} or PLL loop gain can be problematic.

The benefits of the IQ modulator approach are:

- Frequency agility,
- Inherently future-proof, adaptable to become a software-defined radio (SDR),
- Excellent modulation accuracy is possible.

### Generating Analog FM

In this FM application, the IQ Modulator functions as a precise, 360-degree phase modulator. Since phase is the time integral of frequency, a periodically-updated phase accumulator performs the time integral function. ^{2}

The system, illustrated in Figure 1, behaves like a conventional DDS, where the phase accumulator register can both increment and decrement. ^{3} The look-up table (LUT) contains both sine and cosine functions, thus generating a rotating vector of fixed magnitude at a precise phase. This complex signal gets translated upward by the IQ Modulator, to become centered about the LO frequency. For high modulation accuracy, IQ Modulators such as the LTC5599 and LTC5589 require differential baseband drive, easily furnished by the LTC6362 at the required V_{cm}= 1.4V. The DAC reconstruct filters are essential for attenuating DAC Nyquist images due to sampling. By choosing passive LC filter technology, we can potentially reduce the out-of-channel noise floor.

The basic DDS tuning equation can be applied to this application. Notice that we are synthesizing the positive or negative ΔF, which represents the instantaneous frequency deviation:

Where:

*F _{OUT }*= Complex output frequency, Hz. Can be a positive or negative frequency.

*M* = The binary tuning word. Can be a positive or negative number.

*RefClk* = The accumulator update rate, Hz.

*N* = The length of the phase accumulator, bits.

By substituting M= the maximum tuning word, calculating *F _{OUT}* reveals the maximum instantaneous frequency deviation at the modulator output.

Because *F _{OUT}* is typically quite low in many FM applications, for example 5.5 kHz for a NBFM system, the requirement for

*RefClk*is also correspondingly low, in accordance with the DDS equation above. In many cases, the entire angle modulation process becomes practical for implementation in a mixed-signal MCU, interrupt-driven at the

*RefClk*rate. It’s important that when the phase accumulator register overflows or underflows, so does the phase wrap-around, keeping the phase rotation continuous and seamless. This makes precise, DC-coupled FM possible.

### Audio limiting and Pre-emphasis

FM transmitters for analog audio will generally employ limiters which keep the FM from over-deviating and splattering into an adjacent channel. A well-designed system will utilize soft limiting, to minimize audible distortion when this occurs.

White noise at the receiver output would be objectionable if receivers did not have de-emphasis of the high audio frequencies. To compensate for this, transmitters normally utilize audio pre-emphasis at the higher frequencies, for a net overall flat response over the audio passband. ^{4}

Because the IQ Modulator is basically functioning as a precision phase shifter, there are two basic ways to implement pre-emphasis:

- Transmit audio using phase modulation (not FM). This works well; however, limiting of the FM deviation becomes slightly more complex, because the goal is to limit frequency excursions, not phase excursions. An FM input remains useful for encoding sub-audible CTCSS or DCS signaling.
^{5} - Pre-emphasize the audio before FM modulation using an RC network. This is a preferred approach, because deviation limiting is not frequency-dependent.

Whichever method is chosen, additional low-pass and high-pass audio filtering remains necessary for frequencies outside the desired passband.

The FIR filter in a bandpass configuration has the advantage of completely removing the DC frequency error that could otherwise pass through the ADC in the form of a DC offset. This is a nice advantage if high center frequency stability is a requirement.

### Effects of IQ Modulator Impairments

IQ Modulator impairments fall into two overall categories: LO leakage, and Image Rejection (IR).

LO leakage causes the FM baseband vector rotation to wobble off-center, generating AM and spurious products which are related to both the deviation and modulation rate. In general, there are two mechanisms for LO leakage to occur: conducted through the modulator IC, and radiated around the IC. Overall shield effectiveness should be such that the latter is somewhat less than the former.

Image Rejection is a function of quadrature amplitude imbalance, and quadrature phase imbalance. Degradation of either will warp the vector rotation into an elliptical shape, which also generates spurious products related to both deviation and rate.

IQ Modulators such as the LTC5589/99 have a provision to null down both LO leakage and image rejection. For best performance, adjust these registers for lowest FM distortion, and preserve the values in non-volatile memory. Subsequent test results will show how much improvement is typically attainable by this method.

Excessive differential baseband drive also generates undesired output spurious products, typically 3^{rd} order and higher. A small reduction in RF output power can give a much larger reduction in spurious level, and vice-versa.

### A Design Example for NBFM

For the system illustrated in Figure 1, the maximum FM deviation is calculated as follows:

- An 8-bit ADC drives a unity gain FIR filter. Binary output range= -128 to +127.
*RefClk*= the ADC conversion rate

= the phase accumulator update rate

= 196 kHz.*N*= 11 bits

Therefore, Peak FM deviation =

To reduce phase truncation spurs, all 11 accumulator bits map to LUT entries, for a total of 2,048 sine entries, plus 2,048 cosine entries. Each entry is 8-bits wide, matching the resolution of each DAC. LUT initialization occurs only once, at power-up, using floating-point trig functions, with the appropriate scaling and roundoff to match the DAC input range. Once again, this is easily within the capability of a mixed-signal MCU.

In this example, the 11-bit accumulator is 3-bits longer than the 8-bit input, M, from the ADC and FIR filter. Three bits is an acceptable minimum. For a full-scale input transition, the maximum phase change is -128 / (2^{11}) = -1/16^{th} cycle, or -22.5 degrees. Typical phase transitions will be much less. Its desirable to keep maximum phase transitions relatively small, to keep the IQ trajectory path along the constant-power circle, not short-cutting across the circle.

To expedite the construction, baseband differential amplifiers and DAC re-construct filters from a similar project were utilized for this project, having details already documented online. ^{6} Each filter is 5^{th} order, with << 0.5dB passband flatness, while providing at least 35dB attenuation at the Nyquist image frequencies, 190kHz and higher.

### Test Results

Test results for the preceding system, A Design Example for NBFM, are as shown below. The IQ Modulator is an LTC5599 on the factory demo board, with all registers in the default state, except the polyphase center frequency register which is set for the LO frequency in use, 439.44 MHz.

A vector signal analyzer (VSA) is an ideal instrument for testing modulation accuracy. For this testing, the VSA is used to demodulate the IQ Modulator output, as shown in Figure 2. The VSA is in Analog Demodulation mode, displaying instantaneous FM with respect to time, or an FFT of the demodulated FM waveform.

Figure 3 and Figure 4 illustrate the excellent linearity possible with the design. In both figures, the input peak-to-peak amplitude to the ADC is held constant, and we observe the output modulation depth also holds constant.

Figure 5 and Figure 6 illustrate how a FFT of the analog FM output is essential for revealing the spurious products, both before and after adjusting modulator registers to minimize impairments. A slight reduction in baseband drive amplitude would reduce the higher-order spurious products, as noted earlier. For many basic applications, no register adjustments are necessary.

Figure 7 shows frequency error is currently about 96 Hz. This is due to DC offset error at the ADC output. In this example design, 1 LSB contributes ΔF= 196 kHz / 2^{11} = 95.7 Hz. Offset can be eliminated by including a high-pass response in the FIR filter. This same figure also shows the total residual FM of approx. 3 Hz rms, namely due to the lab-grade signal generator for the LO. On-board single-chip PLL solutions will exhibit more than this. The noise spikes in this figure appear randomly, and are believed to be due to ADC offset being slightly more than 1 LSB, but less than 2 LSB.

Figure 8 shows the RF output power and spectrum. RF output power is approx. +0.6dBm. Averaging is used to show the level of DAC image spurious products, in this case about -70dBc. Further reduction is easily attainable by slight increase in *RefClk* frequency.

### Conclusion

Excellent FM modulation accuracy is attainable from a low-power modulator for analog FM applications. For lower bandwidth applications such as audio, an MCU can be used to calculate the FM baseband vectors. DC offset and image suppression registers within the IQ modulator allow adjustment for optimal performance.

### References

^{1} Digital Mobile Radio (DMR) is defined by ETSI standards. See http://www.dmrassociation.org.

^{2} Ref. Boccuzzi, Joseph, *“Signal Processing for Wireless Communications”*, McGraw-Hill, 2008.

^{3} Ref. *“Fundamentals of Direct Digital Synthesis (DDS)”*,

http://www.analog.com/media/en/training-seminars/tutorials/MT-085.pdf

^{4} Ref. EIA-152-C standard for the recommended NBFM pre-emphasis response.

^{5} Continuous Tone-Coded Squelch Systems (CTCSS) and Digital Coded Squelch (DCS) are simple ways to keep interference and undesired signals from opening the squelch at the receiver.

^{6} Ref. “Baseband Design Example for LTC5589/LTC5599 Low-Power IQ Modulator”, http://www.analog.com/en/technical-articles/baseband-design-example-for-ltc5589-ltc5599-low-power-iq-modulator.html