Time delay at 250 Hz bandwidth in FT-1000D and Linrad.
(Mar 02 2009)

#### Signal delay and group delay.

There is a lot to read about filter theory in the literature as well as on the Internet. On this page you will find no mathematics.....

A linear receiver (mode CW or SSB) is just a filter and a frequency shifter. There is no detector. For practical reasons one typically uses several cascaded filters and frequency shifters (mixers.) It is the same in analog and digital receivers.

For reception of a morse coded signal at e.g. 7.010 MHz one might use a filter that allows signals in the range 7.009875 to 7.010125 MHz to pass and one might shift the frequency to place the 250 Hz wide passband from 300 to 550 Hz in the audio range. The time it takes for a signal to pass through a receiver like that, the signal delay, depends on the signal frequency.

To evaluate the signal delay we might send an on-off keyed carrier with a repetition rate of 0.1 Hz and a bandwidth of 1 Hz through the receiver. Assuming that the filter attenuation as well as the signal delay are constants over as little bandwidth as 1 Hz we would find that the signal is totally undistorted by the passage through the filter. The signal would just be delayed a little and attenuated.

If we do such a measurement on a real world receiver we would find that the time delay is independent of the frequency in the flat central region of the filter. As a consequence we would find that the phase shift through the filter grows linearly with frequency in the flat center region (phase shift is frequency multiplied by time.)

On the skirts it may be different. The time delay in analog filters is typically larger on the skirts which means that the phase response is not linear with frequency. With different time delay at different frequencies a signal that contains energy over the entire passband will have its waveform distorted after passing the filter. Now, that is not as bad as one might believe at first. Distorting waveforms is exactly the purpose we want to use the filter for! Consider the output from a filter when the input is a VERY short pulse. One with a spectral content that is totally flat over a much wider frequency range than the filter bandwidth. The output would be a much smaller pulse that is elongated to something in the order of one over the bandwidth. Surely distorted - we filtered away most of the signal energy....

When looking at the details of the pulse response we may find that the filter output is essentially one pulse or we may find an oscillatory behaviour. In analog filters the oscillations represent the longer delay on the filter skirts and these oscillations, ringings, extend longer with steeper skirts in the filter. Only without a flat center region one can get oscillation-free pulse response. Digital filters can be designed for symmetrical impulse response with the ringings both before and after the main pulse. It corresponds to making the delay through the filter the same at all frequencies. This way digital filters can be made to produce a linear phase response.

With a symmetric impulse response the delay measured from the input pulse to the peak of the output pulse would become twice as long compared to a conventional filter having all oscillations after the pulse, but the time from the input pulse until the oscillations on the output have stopped would be essentially the same for filters with similar amplitude responses.

The concept group delay has a mathematical definition as the derivative of the phase shift vs frequency. For real world things that transmit signals like cables or bandbass filters the group delay is the same as the signal delay. The time it takes for energy to pass through the filter.

#### Practical measurements.

With a standard schottky mixer as the keyer the output of a HP8657A was on-off keyed at a slow enough speed to make the separation between consecutive pulses much longer than the time delay through the receiver under test. The RF pulse as well as the loudspeaker output were displayed on a two-channel oscilloscope. In each case two photos are shown below. One with normal signal level during the pulse and another with 40 dB more RF power where the receiver is saturated during the pulse making ringings after the pulse visible down to about -60 dB.

Both the FT-1000D and Linrad were set to a nominal bandwidth of 250 Hz. The measured frequency responses are displayed in figure 1.