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For an AD633 analog multiplier, calculate the ideal output as W = [(X₁ − X₂)(Y₁ − Y₂) / 10 V] + Z. For example, with X = 2 V, Y = 3 V, and Z = 1 V, W = (2 × 3) / 10 + 1 = 1.6 V. The 10 V scale factor matters: the AD633 does not output the unscaled product XY.
What an analog multiplier calculates
An analog multiplier continuously produces an output proportional to the instantaneous product of two analog signals. Unlike a digital multiplier, it does not convert the signals to binary values first. Multipliers are used in signal mixing, modulation and demodulation, phase detection, voltage-controlled gain, squaring, and other analog computations. The AD633 product page lists these among its applications.
For a general multiplier, a useful model is VOUT = K VXVY + VZ. Here K is the scale factor, and VZ is an optional summed signal or offset. If both inputs are expressed in volts, their product has units of volts squared, so K must have units of inverse volts for the output to be a voltage.
AD633 formula and input polarity
The AD633’s nominal transfer function is W = [(X₁ − X₂)(Y₁ − Y₂) / 10 V] + Z. The difference between each pair of inputs is multiplied; Z is then added. The equation and device details appear in the AD633 data sheet.
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If X₂ and Y₂ are connected to the signal reference, then X = X₁ and Y = Y₁, giving W = XY / 10 V + Z. In numerical calculations using volts, this is often written W = 0.1XY + Z. The more explicit denominator, 10 V, makes the units clear. Do not assume a multiplier uses this scale factor: check the selected part’s transfer function.
The AD633 is a four-quadrant multiplier, so either differential input can be positive or negative. With Z = 0, the product is positive when both inputs have the same sign and negative when their signs differ.
| VX | VY | Product sign | Example output |
|---|---|---|---|
| Positive | Positive | Positive | (+2 V × +3 V) / 10 V = +0.6 V |
| Positive | Negative | Negative | (+2 V × −3 V) / 10 V = −0.6 V |
| Negative | Positive | Negative | (−2 V × +3 V) / 10 V = −0.6 V |
| Negative | Negative | Positive | (−2 V × −3 V) / 10 V = +0.6 V |
Calculate the output step by step
- Use the transfer function for the exact multiplier model. For the AD633, start with W = [(X₁ − X₂)(Y₁ − Y₂) / 10 V] + Z.
- Calculate the differential inputs: VX = X₁ − X₂ and VY = Y₁ − Y₂.
- Multiply those differences, then divide by 10 V to apply the AD633 scale factor.
- Add Z, retaining its sign.
- Check the result and input signal peaks against the part’s operating conditions, output swing, and bandwidth.
Example with differential inputs
Let X₁ = 3 V, X₂ = 1 V, Y₁ = 4 V, Y₂ = −1 V, and Z = 0.5 V. Then VX = 2 V and VY = 5 V, so W = (2 × 5) / 10 + 0.5 = 1.5 V.
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Examples with single-ended inputs
| Inputs | Calculation | Ideal output |
|---|---|---|
| X = 4 V, Y = 2 V, Z = 0 | (4 × 2) / 10 | 0.8 V |
| X = −4 V, Y = 2 V, Z = 0 | (−4 × 2) / 10 | −0.8 V |
| X = −4 V, Y = −2 V, Z = 0 | (−4 × −2) / 10 | 0.8 V |
| X = 5 V, Y = 2 V, Z = −1 V | (5 × 2) / 10 − 1 | 0 V |
Squaring
Connect the same signal to both multiplier inputs. For a 3 V input, W = 3² / 10 = 0.9 V. For an arbitrary input V, the ideal output is V² / 10 V. Squaring a bipolar input produces a nonnegative product, though practical offsets and output limits still apply.
Calculating with sine waves
A multiplier operates on instantaneous values, not directly on RMS values. If x(t) = A cos(ω₁t) and y(t) = B cos(ω₂t), their product contains both the sum and difference frequencies:
x(t)y(t) = (AB/2)[cos((ω₁ − ω₂)t) + cos((ω₁ + ω₂)t)].
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For the AD633, divide this expression by 10 V for the product contribution to W. A filter can select the frequency component of interest; without filtering, the multiplier output includes both terms.
Squaring a sine wave
For x(t) = A cos(ωt) applied to both inputs, the AD633 output is w(t) = A²[1 + cos(2ωt)] / 20 V. After low-pass filtering, its DC component is A² / 20 V. Here A is the sine wave’s peak amplitude, not its RMS value. For a sine wave, VRMS = VPK/√2 and VPK = VPP/2.
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Scale factor, gain, and accuracy
The AD633’s nominal output is XY/10 V + Z. If a following amplifier has gain G, the product contribution becomes GXY/10 V, so the system’s effective scale factor is G/(10 V). Include any input attenuation or gain separately when calculating the complete system output.
The equation gives an ideal value, not a guarantee of exact output. The AD633 product page specifies total error within 2% of full scale; this is a full-scale specification, not a blanket claim that every output has 2% relative error. If 10 V is the applicable full-scale output, 2% corresponds to 0.2 V. Consult the device’s specified grade and operating conditions before applying that estimate to a design.
Other contributors include input and output offsets, scale-factor error, X- and Y-input nonlinearity, noise, temperature drift, supply and grounding effects, bandwidth, and clipping. The product page lists approximately 0.4% X-input nonlinearity, 0.1% Y-input nonlinearity, output-referred noise below 100 µV rms over 10 Hz–10 kHz, nominal 1 MHz bandwidth, and 20 V/µs slew rate. These figures have distinct meanings and conditions; do not simply add typical values as though they formed a guaranteed worst-case error.
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Check operating limits before using the result
The AD633 product information lists a supply range of approximately ±8 V to ±18 V, high input resistance of approximately 10 MΩ, and a nominal ±10 V input operating range in its standard application. Those headline figures do not mean every input combination or load permits an output all the way to the supply rails. Use the electrical-characteristics tables in the data sheet for the relevant conditions.
- Check differential input values and waveform peaks, not only DC values or RMS readings.
- Check whether the calculated output plus Z remains within the available output swing under the intended supply and load.
- Allow margin for offsets, error, and transient peaks; an ideal result at the limit may clip in practice.
- Confirm the signal frequency and slew-rate demands. A nominal 1 MHz bandwidth is not a guarantee of full-scale accuracy at every frequency.
- Do not infer single-supply bipolar operation from the transfer equation. Bipolar signals may require a negative rail or a deliberate bias scheme.
- Connect differential inputs and signal references deliberately; floating inputs and poor grounding can cause unpredictable results or added error.
Division and other analog functions
A multiplier can participate in an op-amp feedback circuit that computes a ratio. For example, if the chosen topology makes VFB = VOUTVY/10 V and the op amp forces VFB = VX, algebra gives VOUT = 10 V × VX/VY. That equation describes the stated relationship, not a universal wiring recipe. The valid polarity, denominator range, stability, and scaling depend on the circuit. Follow the divider configuration and conditions in the AD633 data sheet rather than wiring from the algebra alone.
Choose a multiplier for the application
The AD633 is a convenient example for general-purpose calculations, but its speed, accuracy, signal range, and output structure may not suit every design. The table compares alternatives using their manufacturer-published information; specifications apply under the conditions in each product’s documentation.
Quick Recap
| Part | Consider it when | Published distinction | Source |
|---|---|---|---|
| AD633 | A straightforward four-quadrant multiplier is sufficient. | Nominal 10 V scaling; approximately 1 MHz bandwidth; total error within 2% of full scale. | Analog Devices product page |
| AD534 | Precision matters more than simplicity or cost. | The AD534L maximum four-quadrant error is specified at ±0.25%; scale factor is adjustable up to ×100. | Analog Devices product page |
| AD734 | You need higher speed, precision, or direct division features. | 10 MHz full-power bandwidth and 0.1% typical total static error. | Analog Devices product page |
| AD834 | The application is high-frequency signal processing. | DC to more than 500 MHz under specified conditions; differential current-output architecture. | Analog Devices product page |
| MPY634 | You want a wide-bandwidth precision voltage multiplier. | TI lists typical 10 MHz bandwidth and ±0.5% maximum four-quadrant accuracy. | Texas Instruments product page |
Troubleshoot a result that looks wrong
- Output is about ten times the expected value: verify that the AD633’s 10 V denominator was included.
- Sign is wrong: check X₁ − X₂ and Y₁ − Y₂ independently, then include Z with its actual polarity.
- Output differs for an AC signal: establish whether the requested value is instantaneous, peak, peak-to-peak, RMS, or a filtered average.
- Output flattens near a limit: check supply rails, output headroom, input peaks, load, and any Z contribution.
- Small products are inaccurate: offsets and noise can dominate when the ideal product is near zero.
- Unexpected noise or drift: check grounding, references, temperature conditions, and whether any input is left floating.
- Unexpected frequency components: identify the sum and difference products and add the filtering appropriate to the desired signal.
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