# How Gilbert Cell AM modulator Works

In Integrated Circuit(IC) technology, a commonly encountered AM modulator circuit is the differential multiplier based on the Gilbert cell. The Gilbert cell is an adaptable circuit with diverse applications, including its utilization as a balanced AM multiplier circuit when employed in a switching mode. This circuit operates by multiplying the two differential input signals. When employed as a AM balanced modulator, a basic analysis of the circuit can be outlined as follows.

The following shows the circuit diagram of Gilbert Cell AM modulator.

Firstly, we determine the output signal in the absence of the carrier signal. Secondly, we incorporate the carrier signal as the product. The carrier signal is considered to be a high-level switching voltage that alternates the on and off states of transistor pairs Q1, Q4 and Q2, Q3. That is when the carrier signal is high, the transistor Q1, Q4 are conducting and transistors Q2, Q3 are non-conducting. Similarly, when the carrier signal is low, the transistor Q1, Q4 are non-conducting and transistors Q2, Q3 are conducting.

Now consider the current flow in the circuit below.

The current $$I_1$$ and $$I_2$$ are given by,

$$I_1 = I-i_e$$

$$I_2 = I+i_e$$

Therefore the differential voltage is,

$$v_a = v_2-v_1 = R(I_2 - I_1) = 2 i_e R$$

The KVL around the circuit loop which contains the modulating voltage $$m(t)$$ and resistor $$R_e$$, we have,

$$m(t) = V_{be5} +v_e -V_{be6}$$

and since  $$V_{be5} \approx V_{be6}$$

$$m(t) \approx v_e$$

Since the circuit operates with small signal current, $$I >>i_e$$ and therefore,

$$i_e = \frac{v_e}{R_e} = \frac{m(t)}{R_e}$$

Then,

$$v_a = 2 i_e R =\frac{2R}{R_e}m(t)$$

Then the output signal is,

$$v_{out} \approx v_a \times c(t)$$

which is essentially an AM signal.

So this is the working principle of Gilbert Cell AM modulator which are used in AM transmitter and AM receiver. An example of AM modulator IC which uses the Gilbert circuit is the MC1496 balanced modulator. See AM modulator using MC1496.

One can also build AM modulator circuit with single BJT transistor of FET transistor or use diodes. But the balanced Gilbert cell AM modulator offers several advantages over single BJT (Bipolar Junction Transistor) or FET (Field-Effect Transistor) AM modulator circuit. Here are some of the advantages:

1. Improved carrier rejection: The balanced configuration of the Gilbert cell provides better carrier rejection compared to single transistor modulators. It cancels out common-mode signals, such as the carrier, resulting in reduced distortion and improved modulation quality.

2. Higher linearity: The Gilbert cell configuration minimizes distortion and non-linearities in the modulation process. This leads to a more accurate reproduction of the modulating signal on the output.

3. Improved noise performance: The balanced nature of the Gilbert cell helps in common-mode noise rejection, resulting in reduced noise on the modulated signal. This leads to better signal-to-noise ratio (SNR) and improved overall performance.

4. Better frequency response: The Gilbert cell exhibits a wider bandwidth compared to single transistor modulators. It can handle higher-frequency signals more effectively, allowing for a broader range of modulation frequencies.

5. Enhanced isolation: The balanced configuration provides isolation between the modulating signal and the carrier signal, minimizing any interference or cross-talk between the two. This ensures cleaner modulation and improved fidelity.

6. Ease of implementation: The Gilbert cell-based modulators are readily available as integrated circuits (ICs) and are often designed specifically for AM modulation applications. This makes them convenient to use and integrate into larger systems.

Overall, the balanced Gilbert cell AM modulator offers superior performance in terms of carrier rejection, linearity, noise performance, frequency response, isolation, and ease of implementation compared to single BJT or FET modulators.