Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example, if a newborn baby's heart beats at a frequency of 120 times a minute, its period (the interval between beats) is half a second.
Waveform Conversion, Part I - Sine to Square
The system designer is often called upon to convert a sine wave from an oscillator, power splitter, or other RF device into a square wave suitable for driving a logic device. There are numerous acceptable techniques and the best choice will depend upon several factors including the operating frequency, available signal power, available DC power, acceptable edge speeds, and the characteristics of the logic family.
The simplest technique is to directly couple the sine wave into the logic input with a suitable bias circuit. The sine wave should be a few volts p-p for reliable triggering. This technique is most suitable for CMOS devices in the older 4000 series or HC-MOS and only requires a coupling capacitor and two resistors to bias the input to VCC/2. This simple bias scheme should be avoided with AC-MOS devices unless the frequency and amplitude are high and the input signal is always present. Slow-moving or noisy inputs can cause multiple triggers on any gate, however, and Schmitt trigger inputs are recommended when the input sine wave is large enough to overcome the hysteresis. As an example, the 74HC14 Schmitt trigger has a hysteresis voltage of 0.9 volts so an input sine wave should be a couple of volts at a minimum. The simple biased-gate scheme is shown below:
In some instances the input signal is too small to drive the logic devices but sufficient power is available to drive a step-up transformer or matching circuit. One unusual approach uses a series RLC circuit to step up the voltage. At the input frequency, the RLC network simply looks like a resistor since the inductor and capacitor are series resonant. The resistor value is selected to limit the current at resonance (typically 100 ohms) and the inductive reactance is selected to give the desired gate voltage. In the example below, the inductor is selected to give about 5 volts of swing for the signal input current. It is reasonably safe to use the input protection diodes in AC logic to clamp the swing since AC devices are quite immune to latch-up and the input protection circuit is quite robust.
An ordinary RF step-up transformer may also be used to achieve the higher voltage swing and fairly broadband transformers may be constructed on ordinary ferrite beads, pot cores or miniature balun cores.
Although these techniques will give reasonably reliable results, especially when Schmitt trigger inputs are used, more sophisticated approaches may be desired to handle slow-moving signals or wide signal level variation. The following simple two-transistor differential amplifier will give a good square wave for a wide range of sine wave inputs and it has sufficient gain to square up the edges of slower input frequencies. The differential amplifier approach avoids transistor saturation which often limits the speed of single-transistor circuits. Fast diodes may be used to prevent saturation in single-transistor amplifiers but the cost and complexity usually exceeds the addition of another transistor.
Numerous integrated circuit solutions are also available. Line receivers are an excellent choice and are truly designed for the job. The input stages are typically differential amplifiers offering fairly high input impedance and good speed. Some line receivers have built-in voltage dividers allowing the inputs to handle voltages far beyond the power supply rails and some have built-in voltage references for biasing the input stage. They are also available in combination with line drivers and many have tri-state control inputs. The possible choices are numerous - the line driver, receiver data books are among the thicker volumes on the engineer's bookshelf. Beware that many line receivers have built-in frequency response roll-off making them unsuitable for squaring higher frequency oscillators.
The MC1489 is a typical quad line receiver which operates from a single 5 volt supply and can handle input signals from-30 to +30 volts - but the threshold is internally set. This device features a built-in threshold hysteresis of about 0.3 volts (0.9 for the MC1489A) with the lower threshold near one volt. A "response control" pin is provided to shift the threshold points or to add signal filtering.
Another example is the SN55182 which is a dual differential line receiver that also operates from a single 5 volt supply. It is designed to respond to small differential voltages riding on fairly large common-mode voltages and noise. The inputs may be biased to switch anywhere within the 15 volt bipolar common-mode input voltage range. The input impedance is a few thousand ohms but a built-in 170 ohm line-termination resistor is provided. This line receiver's frequency response may also be lowered by adding an external capacitor and a strobe input is available to force the output to a high level. Since many line receivers operate from a single supply and can sense below ground, the schematic can be quite simple. The following circuit shows 1/2 of the SN55182 connected to convert a sine wave centered around ground - typical of transformer or power splitter outputs. The only external component indicated is a 0.1 uF power supply capacitor! It may be desirable to add an additional resistor to ground at the input to match a particular source or cable impedance.
High-speed comparators may also be used in a similar manner to line receivers but the resistor biasing must be done externally and some amount of hysteresis should be added in the form of a feedback resistor from the output to the positive input to ensure positive switching. Some comparators have "totem pole" outputs which are specifically designed to drive TTL and CMOS loads and some have open-collector outputs which only need a pull-up resistor to achieve suitable logic levels.
Many prescaler devices are specifically designed to handle small sine wave inputs and all that is required is a DC blocking capacitor. The designer should be aware that some prescalers will "free-run" or oscillate when no input signal is present.
High frequency sine waves can often be directly applied to ECL inputs with the appropriate bias circuitry if the sine wave amplitude falls within the ECL's voltage specifications. Some ECL devices have a reference voltage output pin which may be used to bias the input. Simply connect a resistor from the reference to the input and capacitor couple the input signal.
Waveform Conversion, Part II - Square to Sine
Oscillators with logic compatible square wave outputs are not suitable for driving many RF devices since the characteristic impedance is usually well below the desired source impedance and the odd harmonics can generate undesired intermodulation products. Converting a square wave to a sine wave is usually accomplished with either a low pass or bandpass filter and a resistor network to achieve the desired impedance. An amplifier at either the input or output of the filter may be necessary to achieve sufficient signal amplitude.The circuit below uses a single resistor and a pi network to generate a 50 ohm sine wave from ordinary CMOS logic. The series resistor is selected to limit the current and to isolate the logic device from the reactive load presented by the pi network. The resistor should be a minimum of 200 ohms for most inexpensive clock oscillators and low-power logic devices and the output sine wave level will be about 4 dBm. If the logic device can supply higher current, a 100 ohm resistor may be used to achieve an output level of 10 dBm. AC devices can drive even heavier loads and >13 dBm outputs are practical with a 68 ohm series resistor. The pi network is selected to match the series resistance to 50 ohms at the operating frequency. The Q of the pi network may be low since a square wave has little second harmonic and the third harmonic is three times the fundamental frequency. A low-Q pi network allows the use of fixed values with no adjustments. Add a DC blocking capacitor in series with the output if the load has a DC path to ground. This capacitor may be left out if the load can tolerate DC current and the decreased efficiency is acceptable.
The values for the components of the pi network may be found in many references but for reference the reactances for Q = 2 at three resistances are as follows:
R = 200 ohms, C1 = C2 = 100 ohms reactance, L = 100 ohms reactance
R = 100 ohms, C1 = 50 ohms reactance, C2 = 41 ohms reactance, L = 65 ohms reactance
R = 68 ohms, C1 = 34 ohms reactance, C2 = 30 ohms reactance, L = 50 ohms reactance
The nearest values with these reactances should work well and the actual resistor may be a bit lower since the logic device will have some internal resistance. If a DC blocking capacitor is added in series with the output it should be selected to have a very low reactance at the operating frequency - typically a 0.1 uF.
An ordinary NPN transistor makes an excellent power amplifier for achieving output levels above 13 dBm with light loading of the logic device as shown in the figure below:
The above circuit draws about 12 mA from the 15 volt supply while providing 17 dBm at 6 MHz. The pi network is set to a Q of 4 and a step-down ratio of 4:1. Other output networks are acceptable including tuned transformers or other matching networks. A grounded-gate JFET may be used in place of the NPN transistor eliminating the need for the two base bias resistors and the base bypass capacitor. The U310 is an excellent JFET for frequencies up to several hundred MHz. Reduce the series resistor if the output amplitude is too low - the JFET has a source resistance much higher that the NPN emitter resistance.
A "Tee" network may be used in place of the pi network shown above with some advantages. Since the gate is driving a series inductor instead of a grounded capacitor, the harmonic loading is much less and a series resistor can often be avoided entirely. In applications where the source impedance is not particularly critical and the maximum signal level is desired the Tee network can give excellent results. The circuit below shows an inexpensive clock oscillator driving a tee network to provide about 2 volts p-p into 50 ohms. The network reactances are for Q = 2 and a transformation ratio near 2.5. The reactance values for other network Qs and transformation ratios may be found in RF handbooks and application notes - one favorite is AN-267 from Motorola.
A resistor may be added in series with the gate output as before to achieve a good output VSWR and to protect the gate against shorted outputs. A DC blocking capacitor in series with one of the inductors is recommended for most applications to reduce the loading on the gate and to prevent DC from reaching the load. If a DC blocking capacitor is added it should be selected to have a very low reactance at the operating frequency - typically a 0.1 uF.
Two-Diode Odd-Order Frequency Multipliers
It is often necessary to multiply the frequency of low noise oscillators without significantly degrading the phase noise beyond the theoretical 20 log (N). Low noise frequency doublers constructed with Schottky signal diodes are readily available but higher-order multipliers often exhibit high flicker noise and poor noise floors due to the nature of the switching device. An odd-order diode multiplier topology published in RF Design magazine allows the use of low noise Schottky diodes to generate odd-order harmonics with very low excess noise. A new, half-wave version of the frequency multiplier is presented along with component values for constructing a 10 to 30 MHz tripler and a 10 to 50 MHz quintupler. The conversion loss for these multipliers is good considering their passive design and the input return loss may be easily optimized for different input levels. The circuit for the multiplier is shown below:
This basic configuration may be used for a wide range of frequencies with odd-order multiplication factors to 7 or more. Many fast-switching diode types may be used with excellent results and the choice will depend upon the signal levels and the required phase noise performance. Schottky-barrier diodes such as the 1N5711 are a good choice for most multiplier applications since the conversion efficiency is good and the phase noise performance is better than all but the best sources. Ordinary silicon switching diodes such as the 1N914 will give slightly better conversion efficiency for output frequencies up to 100 MHz but the phase noise performance may be significantly less than provided by Schottky diodes.
Figures 1 and 2 show the conversion loss for a 10 MHz input multiplied to 30 and 50 MHz. The conversion loss is quite low considering the multiplication factor and the 3x multiplier compares favorably with many frequency doublers.
Tuning Range
Mechanical and/or electrical tuning provisions are provided with most crystal oscillators to adjust the frequency for phase-locking or modulation or to compensate for long-term drift. Mechanical tuning is often accomplished with a single or multi-turn trimmer capacitor or inductor in the crystal circuit which is accessed through a hole in the oscillator housing.
Most Wenzel Associates oscillators employ a varactor diode for all tuning and the mechanical tuning is accomplished internally with a precision potentiometer connected to a precision reference voltage. Our tests have shown that the mechanical stability and hysterisis of the highest quality trimmer potentiometers exceeds the stability of the best precision trimmer capacitors. Electrical tuning is accomplished with the same varactor diode in a configuration yielding high tuning linearity. The mechanical tuning voltage from the potentiometer is applied to the cathode of the tuning diode and the electrical tuning voltage is applied to the anode of the diode through a signal isolating network. The electrical tuning may be centered around zero volts so that in the absence of input the oscillator reverts to the mid-point of the electrical tuning.
As an option, the oscillator's internal reference voltage may be brought out to a pin for connecting to a multi-turn potentiometer for fine tuning. Alternately, a clean DC derived from a separate supply may be applied to the electrical tuning pin. If the available supplies are noisy or unstable, it may be desirable to add a zener diode or reference device and a low-pass noise filter. A temperature compensated zener such as the 1N821 is an excellent choice giving good temperature stability and very low noise - in most instances the 22uF filter capacitor shown below may be left out. Reference devices exhibit excellent stability but they often have rather high noise voltage and the additional filtering is recommended.
- The amount of tuning range that may be provided is a function of the crystal frequency, cut, overtone, and spot size (or motional capacitance). Precision low frequency oscillators using third-overtone SC-cut crystals will have a tuning range of only a couple of PPM whereas large spot size AT-cut fundamental crystals can achieve over a thousand PPM.
- The bandwidth and tuning slope of the electrical tuning input may be specified for PLL applications.
- At the time of shipment oven oscillators may exhibit a daily aging rate which would quickly consume all of the mechanical tuning range. This rapid aging will decrase significantly within a few weeks of operation at the oven temperature.
- Oven oscillators may use high precision, "stiff" crystals since they operate at a single temperature and the tuning only compensates for aging whereas TCXOs must tune far enough to remove temperature effects as well as compensate for aging.
- When an oven oscillator's aging pattern has been established (usually an upward drift) the frequency may be offset in the opposite direction during calibration to nearly double the calibration cycle time.
- Linearity is usually specified as a percentage of the total tuning deviation from a straight line fit to the tuning curve. A 10% linearity specification would allow a deviation of 100 Hz away from the best straight line fit for an oscillator with a 1 kHz tuning range. A potential problem is that this deviation can occur rapidly at one end of the range as shown below. The slope is significantly lower at the top of the curve despite the fact that the oscillator meets a fairly tight linearity specification. For PLL systems where the tuning slope impacts the loop stability, it may be appropriate to specify the minimum and maximum tuning slope at all points on the curve in addition to the percent linearity.
Using Precision Oscillators with External References
Many instruments employing precision crystal oscillators as an internal frequency reference have provisions for accepting an external reference as well. The selection of internal or external may be made by manually throwing a switch or it may be automatically triggered by the presence of signal at the external reference input connector. In the simplest of cases the manual switch simply selects which signal source to direct to the instrument and terminates the unused source with an appropriate resistor. When the internal reference is an oven oscillator, it is often desirable to have a "signal-kill" input to turn the oscillator off while leaving the oven operating. TCXOs and non-compensated oscillators may be turned off when the external reference is present to avoid potential interference.Signal-kill inputs typically accept ordinary TTL levels but they may be configured for custom switching levels without difficulty. Most signal-kill inputs are designed to float to the "on" state when not connected and internal RC circuitry protects the oscillator from damaging voltages or interfering RF signals which might be present on the control line. The circuit shown below will detect the presence of an external reference greater than 1 volt p-p and generate a logic "low" suitable for driving most signal-kill inputs. This control signal could also be used to gate the external input to the instrument's circuitry. The circuit is designed to exhibit a fairly high input impedance so proper cable termination is assumed elsewhere in the instrument.
The following circuit uses the same technique using only two CMOS devices, a 4069 hex inverter and a 4016 or 4066 analog switch. The frequency trimmer potentiometer controls the frequency when no reference is present. The circuit also includes an LED driver to indicate the presence of the external reference signal. Component values are not particularly critical and optimum values will depend upon the application.
Notes:
- The circuit above is operating at the frequency limits of the devices at 10 MHz but the 15 volt supply gives about 12 volts of tuning voltage swing without amplification. HCMOS devices will improve the high frequency performance but the lower 5 volt supply will give a smaller tuning voltage range (under 5 volts). An amplifier could be added for oscillators requiring more tuning voltage swing. To calculate the bandwidth of such a system, multiply the amplifier gain by 1.5 to get the amplified phase slope (the 5 volt squarewave will give a 1.5 volt/radian phase slope) and then multiply by the tuning sensitivity of the oscillator.
- The reference input may require a resistor to ground on the reference side of the 100nF capacitor to properly terminate the input.
- The circuit may be built with tri-state gates but if they are non-inverting gates then a different bias scheme will be required. Remember to bias the external reference gates so that they turn off the tri-state control when no signal is present.
- The oscillator tuning input must be a high impedance (megohms). Add a voltage follower to drive lower impedance inputs.
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