A PSPICE Investigation of 3^rd-Order Distortion

Lab equipment usually used to evaluate or measure IP3 is not usually found on the amateur bench. It most often includes two generators, and a spectrum analyzer. Moving from theory to measurement is a difficult step for all but the most intrepid Amateur investigators.

Circuit simulators such as SPICE can display distortion products as a spectrum analyzer would. Distortion products behave as expected, as does gain compression. For an amateur, SPICE provides a tool to investigate IP3 processes in amplifiers, and mixers.

In this section, a simple amplifier is subjected to an IP3-measuring SPICE simulation. PSPICE, student edition is used. The methods should be transferable to other SPICE platforms.

A review of 3^rd-Order Distortion

Intermodulation is a process where an input signal of one frequency combines with an input signal of another frequency, resulting in signals at still another frequency. The difference in frequency really isn’t required, but some separation helps to separate the two desired signals from distorted output signals. For 3^rd-order intermodulation, two distortion products result from the following combination of the two input signals:

2xF1 – F2

2XF2 – F1

As an example, one input signal is at 7.03 MHz., while the other is at 7.05 MHz. These signals will appear at the amplifier output, accompanied by two 3^rd-order distortion products – one at 7.01 MHz., and another at 7.07 MHz.

We expect that the two desired signals at 7.03 MHz., 7.05 MHz. will be larger at the amplifiers’ output by a factor equal to the power gain. A good amplifier will provide the same power gain for any input signal, regardless of its amplitude. However, for 3^rd-order distortion products, the amplifier displays an equivalent power gain three times larger. As input signals increase, distortion products at the output increase more rapidly.

You can imagine a point where distortion products at the output would have amplitude equal to desired signals. This point describes the 3^rd-order intercept – the amplitude of which is an important figure of merit. Determining the 3^rd-order intercept is the goal of the SPICE simulation described below.

The Amplifier under test

This amplifier is an unremarkable linear Class A wideband amplifier. Unlike a real test setup, we can simply apply two input signals by adding voltage sources in series (or current sources in parallel).

In this case, V1 and V2 are “VSIN” sources with the following parameters:

	V1	V2
DC=	0	0
AC=	0.1	0.1
VOFF=	0	0
VAMPL=	0.001	-0.001
FREQ=	7.03e6	7.05e6
TD =	0	0
DF=	0	0
PHASE=	0	0

A TRANSIENT analysis is done, for a time span of 500 us. A sufficient time must pass so that at least ten cycles of the difference frequency (in this case, 20 KHz) is displayed. PSPICE displays output voltage amplitude as an oscilloscope would – voltage vs. time, by default:

On this same display screen, you may select “FFT” to display output as a spectrum analyzer would. Choose a logarithmic vertical display, and set horizontal span from 7.0 MHz. to 7.1 MHz.:

The noise floor rests somewhat below 0.1uV here. This isn’t the noise floor of the amplifier, but of the Fourier analyzer. Only two signals show above this noise, with no distortion products visible. The amplitude of the two signals appear to be:

V1 @ 7.03 MHz. = 1.988 mV

V2 @ 7.05 MHz. = 1.987 mV

Available generator voltage is 0.5mV, giving available power of –53 dBm

Power delivered to the 50 ohm load is (1.988e-3)²/50 = -41 dBm

Power gain is 12 dB

Let’s run this simulation again, with higher amplitudes at V1 and at V2 – say 30 mV each, pushing the amplifier to exhibit a little distortion. Looking at the output, at the 50 ohm load:

Now the IP3 distortion products appear above the noise floor, although they’re still much smaller than the desired signals. On the “amplitude vs. time” display, you wouldn’t see a hint of these distortion products. Let’s catalog the amplitude of all four signals:

IP3lower @ 7.01 MHz. = 10.13uV (-86.88 dBm)

V1 @ 7.03 MHz. = 59.6mV (-11.48 dBm)

V2 @ 7.05 MHz. = 59.6mV (-11.48 dBm)

IP3upper @ 7.07 MHz. = 10.08uV (-86.92 dBm)

With 15 mV (-23.47 dBm) available from each source, gain is 11.99 dB as before.

Another simulation is run, with still higher input amplitudes at V1 and at V2 of 60 mV:

This looks similar to the previous run at half the amplitude, but we should see distortion products gaining ground on the main signals:

IP3lower @ 7.01 MHz. = 93.87 uV (-67.54 dBm)

V1 @ 7.03 MHz. = 119.02 mV (-5.48 dBm)

V2 @ 7.05 MHz. = 118.99 mV (-5.48 dBm)

IP3upper @ 7.07 MHz. = 94.66 uV (-67.47 dBm)

With 30 mV (-17.47 dBm) available from each source, gain is still 11.99 dB as before.

Compare this case with the previous run (at half the amplitude). Legitimate output signals are 6 dB higher, as expected. The IP3 signals came up 19.34 and 19.45 dB respectively, whereas we’d expect them to come up 18 dB.

We have more than enough information now to find the 3^rd – order intercept. One of the previous two runs is sufficient to find this result:

Intermodulation Dynamic Range = 2x( IP3out – Pout)

Intermodulation Dynamic Range is the ratio of desired signal to undesired signal. Let’s take our second case where desired output was –5.48 dBm, and undesired output was –67.5 dBm. The ratio here is 62.02 dB.

Pout is the power out of one of the desired signals, -5.48 dBm.

Rearranging to find 3^rd-order intercept at the output, IP3out,

IP3out = (ImDR + 2xPout) / 2

= (62.02 - 10.96) / 2

= +25.5 dBm

The input intercept IP3in would be lower by a factor equal to amplifier gain: IP3in = +13.5 dBm

This PSPICE simulation can also examine gain compression too. Many runs were made at many different generator amplitudes to give output signals shown in the following graph:

It should be clear that at large amplitudes, where gain begins to drop from 12 dB, distortion products no longer follow the three-times rule. At large amplitudes, distortion products can’t be reliably used to find IP3. Furthermore, the concept of 3^rd-order intercept is not achievable in practice, since the amplifier cannot actually deal linearly with such large signals.