Transmitters
3.6 FIGURES AFFECTING RADAR PERFORMANCE
3.6.4 Stability
The stability of the transmitted pulse depends on the reproducibility of its timing, amplitude, radio frequency, and phase.
The requirement for stability depends on the signal processor used. The times in question are:
• From one pulse to the next pulse;
• During one coherent processing interval (CPI).
Each radar transmitter is different and only a typical master oscillator power amplifier (MOPA) transmitter is shown here. The analysis and summing of the various components are an exact bookkeeping operation and are best carried out using a spreadsheet. It is assumed in this section that the transmitter receives its triggers and transmitter frequency (pulse) signal from an outside unit. Any signals at the radar frequency in the transmitter frequency are best switched off until they are needed, as they represent the perfect jammer signal.
The transmitted pulse timing depends on the timing of the modulator, which forms the driving pulse in radars with a power amplifier or on the modulator pulse with magnetron radars. Errors in the timing are called jitter. The timing may be at exact or random intervals within a range, or jittered. The latter timing was used in older, simpler radars to reject repeater jamming. A typical block diagram for the power amplifier stages was shown in Figure 3.1. How this affects transmitter stability is shown in the simple example in Figure 3.31.
The sections that follow contain an example used to estimate the stability of a transmitter for a radar. There are a number of delays that contain an element of jitter that is different for each counter chain.
3.6.4.1 Trigger generation
The transmitter pretrigger is normally derived from and resynchronized with the coherent oscillator (COHO) (see Chapter 1). The trigger passes through a number of gates, each of which adds to the jitter in a random manner. The total standard deviation of the jitter is the sum of the squares of the individual components. For example, if there are four gates between the reference point and the radio frequency modulator and each has a jitter of 50 ps, the total jitter at A in Figure 3.31 is
This neglects the jitter in the following linear amplifier stages. The limiting cancellation ratio (CR ) caused by timinglim is given by [7]
4 gates Radio frequency modulator
Driver Output
stage
Modulator
7 gates Pulse former
100 ps Radio frequency in
Pulse position jitter 100 ps
Pulse width jitter 176 ps
Output Driver, additionally
Amplitude 600 µV in 12 V Phase 13 µrad
Transmitter pretrigger
Radio frequency modulator Amplitude 600 µV in 12 V Phase 13 µrad
A
B
C D
E F
G
66.1 ps
Radio frequency pulse position
Modulator pulse jitter 752.9 ps Effective variation in modulator pulse voltage
CRtiming ' 20 log10 10&6 100 × 10&12
1 2
dB ' 76.990 dB
CRfrequency ' 20 log10 1
B )ft Jt
CRfrequency ' 20 log10 1
B 100 . 10&6 dB ' 70.07 dB
Figure 3.31 The components of transmitter stability.
(3.19)
(3.20)
(3.21) where J is the transmitter pulse length;
)J the standard deviation of the pulse jitter;
BJ is the time-bandwidth product (or pulse compression ratio) or unity where pulse compression is not used.
The limiting cancellation ratio for a 1 µs pulse caused by 100 ps timing jitter is given by
3.6.4.2 Transmitter frequency
The change of transmitter frequency from pulse to pulse limits the cancellation ratio to
where )f is the transmitter frequency change between pulses;t Jt is the transmitter pulse width.
A frequency drift of 100 Hz between pulses gives
Jitter for 50 counts ' 50 . 25 ps ' 176.777 ps
CRpulsewidth ' 20 log10 J
)pulse width 1 BJ
dB
CRpulsewidth ' 20 log10 10&6 176.777 × 10&12
1 1
dB ' 75.051 dB
Amplitude variation ' 600 × 10&6
12 ' 0.005 %
CRrfmod amp ' 20log10 12
600 × 10&6 dB ' 86.021 dB
Phase variation ' 7.5 × 2 × 0.005
100 ' 0.00075 degrees ' 13.090 µradians
CRrfmod phase ' 20log10 1
13.090 × 10&6 dB ' 97.661 dB
(3.22)
(3.23)
(3.24)
(3.25)
(3.26) 3.6.4.3 Radio frequency modulator
The radio frequency (RF) modulator is responsible for forming the radio frequency pulse that will be amplified and transmitted. The leading edge is assumed to have the jitter of the pulse from the fourth gate of the preceding stage. A stop trigger defines the end of the pulse. If, for example, this is achieved with 50 counts, there will be a pulse width jitter (B in Figure 3.31) of
This limits the cancellation ratio to
This case gives
At this stage, it is normal to form the leading and trailing edges of the pulses to reduce interfering sidebands as shown in Section 3.3.
The voltage from the stabilized power supplies in this block have a noise like voltage variation. It is assumed that each block is supplied from an independent power supply so that the power supply noise voltages add only in the root mean square (rms) sense. For example, an rms noise of 600 µV on a 12 V power supply gives a variation of
There is also phase variation from the modulator block with supply voltage. If this is 7.5 degrees for a 3 dB change in output caused by low power supply voltage, the phase error is
3.6.4.4 Driver
The driver stages for the radio frequency pulses carry relatively low powers and are supplied by stable power supplies with a voltage variation similar to noise. As with the radio frequency modulator, the power supplies amplitude and phase modulate the output from the driver. The example assumes 600 µV in 12 V and 13 µradians in phase.
CRoutput amp ' 20log10 A )A dB
CRoutput phase ' 20log10 1 )N dB
(3.27)
(3.28) 3.6.4.5 Modulator trigger generation
The pulse modulator stores electrical energy during the interpulse period and releases it as necessary for the output stage.
This process takes time, so that pretriggers are required to time the pulse-forming operation in time for the transmitter pulse. In the example, there are seven gates using different components as in Section 3.6.4.3, each with 25 ps jitter, giving an rms total of 66.14 ps at point E in Figure 3.31.
3.6.4.6 Pulse modulator
The modulator output pulse switches on the output stage, so the direct current can stabilize before the radio frequency drive is applied. The radio frequency drive is applied and then ends. Soon after this point in time, the modulator has discharged or is switched off.
The variation or jitter in the switching times may be grouped as follows:
• Trigger amplification;
• Jitter in the main thyristors or other switches.
The effect of the jitter is to move the modulator pulse with respect to the radio frequency driver pulse. If the modulator pulse had a flat top, there would be no problem. Normally, modulator pulses droop from start to finish, so this movement represents a change of amplitude. The modulator also has amplitude and phase modulating effects on the output stage caused by amplitude and timing variations. In the example this jitter is taken to be 750 ps, which added to the jitter in Section 3.6.4.5 gives 752.9 ps at point F in Figure 3.31. These effects are discussed under output stage in the next section.
3.6.4.7 Output stage
The reproducibility of the amplitude of the transmitted pulse is determined primarily by the modulator of the output stage.
The waveforms are often not very square but must be the same from pulse to pulse. The variation in the amplitude of the modulator pulses gives echoes of varying amplitudes which a signal processor may mistake for a Doppler frequency.
The limit on the cancellation ratio is given by [7]
where A is the pulse amplitude, V;
)A is the standard deviation of the pulse amplitude, V.
In a master oscillator power amplifier transmitter (MOPA) the reproducibility of the phase of the transmitted pulse is determined primarily by the sources of the radio frequency [7]. These are the coherent and local oscillators (COHO and LO or STALO). Magnetron radars transmit with random phase, and the phase stability is determined by the accuracy of either a rephased coherent oscillator or the phase corrector. This phase error limits the cancellation ratio as
where )N is the standard deviation of the phase error in radians between pulses.
This example uses a klystron output stage. The main components of the amplitude and phase errors are as follows:
• Heater voltage.
With the trend to smaller components the heater supply frequency may be in the order of many kilohertz. In indirectly heated tubes, this voltage couples capacitively with the cathode and adds to the anode voltage, giving a different voltage during each pulse. This may be reduced by rectifying the heater power or by switching it off
1 CRtransmitter
' 1
CRtiming % 1
CRfrequency % 1
CRpulsewidth
% 1
CRrfmod amp % 1
CRrfmod phase
% 1
CRoutput amp % 1
CRoutput phase
(3.29) completely during the transmitter pulse. In the example, the heater to cathode isolation is assumed to be 53 dB.
• Magnetic field.
As with the heater voltage, the trend is for small components running at higher frequencies to supply the current, normally many ampères, for the solenoids for the magnetic field (excluding triodes, pentodes, transistors, and so on).
A change of magnetic field changes the phase at the output and may be fast enough for a change between pulses.
• Cathode voltage.
This is supplied from the modulator, often through a transformer. Each pulse from the modulator has a different amplitude, which is translated into a phase error. The transformer may not return to exactly the same rest state between pulses. This remaining random component of the magnetic field adds to the field from primary winding carrying the modulator pulse.
• Timing of modulator and radio frequency pulses, anode voltage droop.
In the example, the droop of the modulator pulse is taken to be 3% in 1 µs. When the modulator pulse jitter is 752 ps the limitation in cancellation ratio reciprocal is 2.10 .-5
The output stages thus give amplitude and phase errors that limit the cancellation ratio of the radar. An example is given in Table 3.4.
3.6.4.8 Omitted components
Each transmitter is different. The timing uncertainty caused by cable-length tolerances, actual connector resistances, saturable reactors, and many other types of components has been omitted here, as have the magnetization variations and tolerances of the transformers.
3.6.4.9 Summing the components in Table 3.4
The components for stability are expressed as fractions that represent standard deviations or the reciprocal of the individual cancellation ratio limitations. Amplitude and phase variances are summed to give the final standard deviations, which assumes that they are not correlated. In the case of power supply ripple, the amplitude and phase errors must be added linearly if the components are fed from a common power supply. Switching power supplies normally operate at different frequencies, so the ripple of the power supplies is not synchronous.
Once the fractions for timing, pulse width, frequency, amplitude, and phase have been calculated, they can be added to give a final reciprocal of the cancellation ratio limitation.
The total limitation of the cancellation ratio for Chapter 14 for the transmitter, where there is no correlation between the various factors, is given by
As an example, if each of the five components has the value 67 dB, then the combined result for Chapter 14 is 60 dB.
Table 3.4
The stability calculation in spreadsheet form
Section Parameter Timing, ps Frequency, Amplitude Phase, Cancellation
Hz radians ratio
limitation, dB Factors affecting pulse timing
3.6.4.1 Pulse timing 100 ps 0.0001 76.990
Factors affecting radio frequency
3.6.4.2 Radio frequency change between pulses 100 Hz 0.0001 80.000
Factors affecting pulse width
3.6.4.3 Pulse width variation 122.4 ps 0.0001 78.244
Factors affecting radio frequency pulse amplitude and phase 3.6.4.3 Radio frequency Modulator
Amplitude 0
Phase 0
3.6.4.4 Driver
Amplitude 0
Phase 0
3.6.4.5 Modulator trigger
Amplifying gates 7 gates @ 25 ps = 66.144 ps 3.6.4.6 Pulse modulator
Thyristors 750 ps
Total 752.91 ps
3.6.4.7 Output stage Heater voltage
Amplitude 7.07V 53dB isolation 0
Phase 45% for 80 kV 6.40e-09
Anode voltage
Amplitude 0.004% of 80 kV 0
Phase 45% for 80 kV 0
Anode voltage droop
Amplitude 3% in 1µs times modulator jitter (752.9 ps) 0
Phase 45% for 80 kV 0
Solenoid current Amplitude
Phase 0.2° for 1% current 0
5 mA in 20 A --- ---
rms sum 0 0
Limits to cancellation ratio dB 81.484 80.366
Fraction dB
Limit to cancellation ratio caused by pulse timing jitter 0.0001 76.990
Limit to cancellation ratio caused by pulse width variation 0.0001 78.244
Limit to cancellation ratio caused by pulse amplitude variation 0 81.484
Limit to cancellation ratio caused by pulse phase variation 0 80.366
Limit to cancellation ratio caused by radio frequency variation 0.0001 80.000
--- ---
Total cancellation ratio 0.0005 66.021 66.021