SPICE simulations of regenerative detector sensitivity

This post details simulation results of a 1.2-volt BJT regenerative detector, showing the AF output voltage at the detector for input RF voltages of 1 microvolt, 10 microvolts, and 100 microvolts. These simulations are part of my continuing experiments with 1.2-volt AGC. The AF input level into the AGC detector determines the control voltage and the amount of gain reduction that the AGC can achieve. Therefore, in designing an AGC system, it is important to quantify the amount of AF output that the RF detector can deliver.

Notes on the simulation procedure

1. The general idea of these simulations is to adjust the regeneration level to be barely oscillating, for above-threshold synchronous reception. Then, an AM signal (100% modulation with a 1 kHz audio frequency) is generated at the oscillator's resonant frequency, and this AM signal is inductively coupled into the tank.
2. To accurately determine the oscillator's resonant frequency, the simulation must be run at high temporal resolution with no waveform compression. "High temporal resolution" subjectively means that zooming into the traces of the RF signal should show very smooth curves over an entire RF cycle -- in other words, each smooth RF cycle should be approximated by several tens of timesteps. In the below simulations, the radio frequency is around 2 MHz. This means that one cycle of the RF voltage is completed in 0.5 microseconds, or equivalently 500 nanoseconds. By selecting a timestep of 10 nanoseconds, there will be 50 discrete steps available to simulate each RF cycle. In other words, the smooth curve of one RF cycle will be approximated by 50 straight-line segments. 
3. With a high-temporal-resolution, run a transient simulation and allow the oscillator to barely oscillate. The regeneration level corresponding to "barely oscillating" must be found experimentally. A voltage pulse is used in series with the tank coil to "kick-start" the oscillator. With the oscillator barely oscillating, an FFT is taken on the transient (time-domain) data to give the frequency-domain response. Zooming into the peak on the FFT will give the frequency of the oscillator. The frequency should be determined to better than 1 Hz accuracy.
4. Given the oscillator's resonant frequency, then an AM signal at that same frequency can be coupled into the tank for regenerative amplification and detection. If the frequency is slightly off, you will get "beating" effects where the oscillator's frequency beats against the slightly-mismatched incoming signal to generate an audio-frequency beat note. This is undesirable and complicates the interpretation of the results; hence, the need to accurately determine the oscillator's frequency as described in step 2. 
5. The audio-frequency output should be visible at the output of the regenerative detector. 
6. The first 1 second of simulated circuit's behavior (i.e. the first 100,000,000 timesteps with a timestep of 10 nanoseconds) shows widely varying circuit voltages, as the circuit requires time to reach steady-state (capacitors need to be charged, bias levels need to stabilise, and so forth). Therefore, the first 1 second of simulation data is discarded, and data is saved from 1 second to 1.5 seconds.
7. The regenerative detector circuit itself is a common-base oscillator at 2 MHz with AF output taken from the collector. Similar circuits can be seen here: http://www.ke3ij.com/bigloop.htm, http://www.techlib.com/electronics/regen.html. The future plan is to use the 2-MHz regenerative detector as the IF stage in a superheterodyne receiver, with AGC controlling the amount of signal that is fed into the regenerative detector. The regenerative detector's audio-frequency output is fed into a 3-transistor AF amplifier, which will eventually be used to generate a control voltage as part of the AGC scheme.
8. Using the circuit simulator software LTspice IV, this simulation took between 1 and 2 hours to run. Typical simulation speed was usually such that computing 1 millisecond of simulated time required 1 actual second (wall-clock time) of execution time. Given this simulation speed, three simulation runs, each 1500 ms long, yield an estimated total simulation time of about 1.25 hours. The results occupy 36 gigabytes of disk space.

The circuit under simulation

Q1 is the regenerative detector, running off of 1.2 volts.

Rs (1 ohm) represents series losses in the inductor L1. Oscillation frequency was determined by an FFT to be 2.0178 MHz. With L1=25 uH, this implies a coil Q of 317. This is fairly high and might be difficult to achieve in practice. It might be more realistic to increase Rs to 2 ohms for a coil Q of 158, which is more reasonable for small-form-factor coils like those wound on iron-powder toroidal cores.

Regeneration is controlled by the resistive voltage divider R3/R4.

Unamplified AF output from the regenerative detector is taken from the collector load resistor R1.

Amplified AF output (amplified by Q2, Q3, and Q4) is available at the top of R12. In a later project, the amplified AF output will also be taken from C9 to drive an AGC detector and generate an AGC control voltage.

Simulation results

Amplitude-modulated RF input to the regenerative detector

The simulation is run with three different values for the RF input voltages: 100 uV peak, 10 uV peak, and 1 uV peak, as shown below.

Unamplified AF output from regenerative detector

The unamplified AF output at the detector's collector resistor is as follows. The red trace corresponds to an input RF voltage of 1 microvolt peak; the blue, 10 microvolts; the green, 100 microvolts.

If we zoom in temporally and observe only a 10 ms window of the output, the AF signal becomes clearly visible. We have one cycle per one millisecond -- i.e., a 1 kHz AF output, corresponding to the 1 kHz-modulated AM signal that was fed into the tank.

Zooming in closer to the red trace gives the following result.

Though somewhat difficult to see, the red trace is also varying upward and downward at a rate of 1 kHz. Observing the top edge of the red trace, it can be seen that each small peak (rise in voltage) on the top edge is simultaneously accompanied by a peak (rise in voltage) of the bottom edge. Therefore, the top edge and bottom edge of the red trace, at audio-frequencies, are essentially moving in unison, and therefore to understand the amplitude of the AF component of the red trace, we can simply look at the amplitude variations on the top edge of the red trace.

Zooming in even closer to the top edge of the red trace gives this result, where we can clearly see the 1-kHz audio-frequency variation in output voltage.

Input-to-output linearity of regenerative detector

Observing the above graphs we get the following numerical results:

• For a 1 uV peak (2 uV peak-peak) 100%-modulated AM signal as input, the detector's AF output is about 15.47 uV peak-peak. This represents about 17.7 dB of gain.
• For a 10 uV peak (20 uV peak-peak) 100%-modulated AM signal as input, the detector's AF output is about 199 uV peak-peak. This represents about 20 dB of gain. Comparing these results with the previous case, the input has increased only 20 dB from 1 uV to 10 uV, but the output has increased about 22.2 dB from 15.47 uV to 199 uV.
• For a 100 uV peak (200 uV peak-peak) 100%-modulated AM signal as input, the detector's AF output is about 2.294 mV peak-peak. This represents about 21.2 dB of gain. Comparing these results with the previous case, the input has again increased only 20 dB from 10 uV to 100 uV, but the output has increased about 21.2 dB from 199 uV to 2.294 mV.

So some detector non-linearity is evident. To quantify this further, it would also be possible to run a two-tone test in the simulator to determine third-order intermodulation performance. This goes beyond the scope of this article.

Observing the temporal simulation resolution

Zooming in temporally (observing a less-than-1-millisecond window of the output), we can see that the apparently smooth traces of the AF signal actually still have a radio-frequency component -- a residual of the original RF signal. The RF component is small, but present.

 Zooming in even further, we observe the individual peaks and troughs of the RF component of the AF output.

Zooming in to one peak of the RF component of the AF output, we can begin to see the discrete lines that form the approximation to the smooth curve of the continuous RF signal.

Output of AF amplifier

Q2, Q3, and Q4 amplify the small AF output from Q1. The results are as follows.

Observing a 10-ms window from 490 ms to 500 ms gives the following signal at the "hi" output of the AF amplifier.

We can see in the above diagram that larger input signal levels (blue trace corresponding to 10 uV RF input; green trace corresponding to 100 uV RF input) are distorted after amplification. This is why the planned receiver will use AGC: to attenuate larger input signals before they can drive the AF amplifier (or the regenerative detector) into distortion.

Zooming in closer to the red trace (corresponding to 1 uV RF input) gives the following result, a fairly clean sine wave corresponding to the original 1 kHz modulation on the input RF signal.

Zooming in to one peak of the red trace, we again see the residual RF component in the amplified AF signal. For this reason it is important to separate RF and AF wiring in a regenerative receiver; otherwise, some RF from the audio amplifier might couple back into the tank, causing unwanted feedback, difficult-to-control regeneration, and other unpredictable effects.

Appendix

Although my regenerative detector circuit uses a fixed voltage divider to determine the base bias, it should be noted that similar circuits at http://www.ke3ij.com/bigloop.htm, http://www.techlib.com/electronics/regen.html use collector feedback biasing, whereby the top half of the base's voltage divider is connected not directly to Vcc, but instead to the collector resistor.

It is possible that collector feedback biasing will have an effect on the amount of AF output available at the detector's collector. More simulations are needed to confirm this.